Factors of 140

Factors of 140

Factors are numbers that can be multiplied together to get a given number. In this blog, we will explore the factors of 140 and understand their significance in mathematics.

Answer to Factors of 140

The factors of 140 are: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140.

How to solve the problem: hints

To find the factors of 140, we can follow these steps:

1. Determine the criteria for judging whether a number is a factor. A number is a factor of 140 if it divides 140 without leaving a remainder.

2. List all the numbers starting from 1 up to the given number, which is 140 in this case.

3. Use each number as a divisor and verify whether it is a factor by dividing 140 by the number. If the division is exact, without any remainder, then the number is a factor.

4. Finally, collect all the numbers that are factors of 140.

Let's now go through a step-by-step solution to find the factors of 140.

Step-by-step solution

1. We start by listing all the numbers from 1 to 140.

2. Using each number as a divisor, we divide 140 and check if the division is exact.

   • 1 is a factor of 140 because 140 ÷ 1 = 140.
   • 2 is a factor of 140 because 140 ÷ 2 = 70.
   • 3 is not a factor of 140 because 140 ÷ 3 = 46.67 (not an exact division).
   • 4 is a factor of 140 because 140 ÷ 4 = 35.
   • 5 is a factor of 140 because 140 ÷ 5 = 28.
   • 6 is not a factor of 140 because 140 ÷ 6 = 23.33 (not an exact division).
   • 7 is a factor of 140 because 140 ÷ 7 = 20.
   • 8 is not a factor of 140 because 140 ÷ 8 = 17.5 (not an exact division).
   • 9 is not a factor of 140 because 140 ÷ 9 = 15.56 (not an exact division).
   • 10 is a factor of 140 because 140 ÷ 10 = 14.
   • 11 is not a factor of 140 because 140 ÷ 11 = 12.73 (not an exact division).
   • 12 is not a factor of 140 because 140 ÷ 12 = 11.67 (not an exact division).
   • 13 is not a factor of 140 because 140 ÷ 13 = 10.77 (not an exact division).
   • 14 is a factor of 140 because 140 ÷ 14 = 10.
   • 15 is not a factor of 140 because 140 ÷ 15 = 9.33 (not an exact division).
   • 16 is not a factor of 140 because 140 ÷ 16 = 8.75 (not an exact division).
   • 17 is not a factor of 140 because 140 ÷ 17 = 8.24 (not an exact division).
   • 18 is not a factor of 140 because 140 ÷ 18 = 7.78 (not an exact division).
   • 19 is not a factor of 140 because 140 ÷ 19 = 7.37 (not an exact division).
   • 20 is a factor of 140 because 140 ÷ 20 = 7.
   • 21 is not a factor of 140 because 140 ÷ 21 = 6.67 (not an exact division).
   • 22 is not a factor of 140 because 140 ÷ 22 = 6.36 (not an exact division).
   • 23 is not a factor of 140 because 140 ÷ 23 = 6.09 (not an exact division).
   • 24 is not a factor of 140 because 140 ÷ 24 = 5.83 (not an exact division).
   • 25 is not a factor of 140 because 140 ÷ 25 = 5.6 (not an exact division).
   • 26 is not a factor of 140 because 140 ÷ 26 = 5.38 (not an exact division).
   • 27 is not a factor of 140 because 140 ÷ 27 = 5.19 (not an exact division).
   • 28 is a factor of 140 because 140 ÷ 28 = 5.
   • 29 is not a factor of 140 because 140 ÷ 29 = 4.83 (not an exact division).
   • 30 is not a factor of 140 because 140 ÷ 30 = 4.67 (not an exact division).
   • 31 is not a factor of 140 because 140 ÷ 31 = 4.52 (not an exact division).
   • 32 is not a factor of 140 because 140 ÷ 32 = 4.38 (not an exact division).
   • 33 is not a factor of 140 because 140 ÷ 33 = 4.24 (not an exact division).
   • 34 is not a factor of 140 because 140 ÷ 34 = 4.12 (not an exact division).
   • 35 is a factor of 140 because 140 ÷ 35 = 4.
   • 36 is not a factor of 140 because 140 ÷ 36 = 3.89 (not an exact division).
   • 37 is not a factor of 140 because 140 ÷ 37 = 3.78 (not an exact division).
   • 38 is not a factor of 140 because 140 ÷ 38 = 3.68 (not an exact division).
   • 39 is not a factor of 140 because 140 ÷ 39 = 3.59 (not an exact division).
   • 40 is not a factor of 140 because 140 ÷ 40 = 3.5 (not an exact division).
   • 41 is not a factor of 140 because 140 ÷ 41 = 3.41 (not an exact division).
   • 42 is not a factor of 140 because 140 ÷ 42 = 3.33 (not an exact division).
   • 43 is not a factor of 140 because 140 ÷ 43 = 3.26 (not an exact division).
   • 44 is not a factor of 140 because 140 ÷ 44 = 3.18 (not an exact division).
   • 45 is not a factor of 140 because 140 ÷ 45 = 3.11 (not an exact division).
   • 46 is not a factor of 140 because 140 ÷ 46 = 3.04 (not an exact division).
   • 47 is not a factor of 140 because 140 ÷ 47 = 2.98 (not an exact division).
   • 48 is not a factor of 140 because 140 ÷ 48 = 2.92 (not an exact division).
   • 49 is not a factor of 140 because 140 ÷ 49 = 2.86 (not an exact division).
   • 50 is not a factor of 140 because 140 ÷ 50 = 2.8 (not an exact division).
   • 51 is not a factor of 140 because 140 ÷ 51 = 2.75 (not an exact division).
   • 52 is not a factor of 140 because 140 ÷ 52 = 2.69 (not an exact division).
   • 53 is not a factor of 140 because 140 ÷ 53 = 2.64 (not an exact division).
   • 54 is not a factor of 140 because 140 ÷ 54 = 2.59 (not an exact division).
   • 55 is not a factor of 140 because 140 ÷ 55 = 2.55 (not an exact division).
   • 56 is not a factor of 140 because 140 ÷ 56 = 2.5 (not an exact division).
   • 57 is not a factor of 140 because 140 ÷ 57 = 2.46 (not an exact division).
   • 58 is not a factor of 140 because 140 ÷ 58 = 2.41 (not an exact division).
   • 59 is not a factor of 140 because 140 ÷ 59 = 2.37 (not an exact division).
   • 60 is not a factor of 140 because 140 ÷ 60 = 2.33 (not an exact division).
   • 61 is not a factor of 140 because 140 ÷ 61 = 2.3 (not an exact division).
   • 62 is not a factor of 140 because 140 ÷ 62 = 2.26 (not an exact division).
   • 63 is not a factor of 140 because 140 ÷ 63 = 2.22 (not an exact division).
   • 64 is not a factor of 140 because 140 ÷ 64 = 2.19 (not an exact division).
   • 65 is not a factor of 140 because 140 ÷ 65 = 2.15 (not an exact division).
   • 66 is not a factor of 140 because 140 ÷ 66 = 2.12 (not an exact division).
   • 67 is not a factor of 140 because 140 ÷ 67 = 2.09 (not an exact division).
   • 68 is not a factor of 140 because 140 ÷ 68 = 2.06 (not an exact division).
   • 69 is not a factor of 140 because 140 ÷ 69 = 2.03 (not an exact division).
   • 70 is a factor of 140 because 140 ÷ 70 = 2.
   • 71 is not a factor of 140 because 140 ÷ 71 = 1.97 (not an exact division).
   • 72 is not a factor of 140 because 140 ÷ 72 = 1.94 (not an exact division).
   • 73 is not a factor of 140 because 140 ÷ 73 = 1.92 (not an exact division).
   • 74 is not a factor of 140 because 140 ÷ 74 = 1.89 (not an exact division).
   • 75 is not a factor of 140 because 140 ÷ 75 = 1.87 (not an exact division).
   • 76 is not a factor of 140 because 140 ÷ 76 = 1.84 (not an exact division).
   • 77 is not a factor of 140 because 140 ÷ 77 = 1.82 (not an exact division).
   • 78 is not a factor of 140 because 140 ÷ 78 = 1.79 (not an exact division).
   • 79 is not a factor of 140 because 140 ÷ 79 = 1.77 (not an exact division).
   • 80 is not a factor of 140 because 140 ÷ 80 = 1.75 (not an exact division).
   • 81 is not a factor of 140 because 140 ÷ 81 = 1.73 (not an exact division).
   • 82 is not a factor of 140 because 140 ÷ 82 = 1.71 (not an exact division).
   • 83 is not a factor of 140 because 140 ÷ 83 = 1.69 (not an exact division).
   • 84 is not a factor of 140 because 140 ÷ 84 = 1.67 (not an exact division).
   • 85 is not a factor of 140 because 140 ÷ 85 = 1.65 (not an exact division).
   • 86 is not a factor of 140 because 140 ÷ 86 = 1.63 (not an exact division).
   • 87 is not a factor of 140 because 140 ÷ 87 = 1.61 (not an exact division).
   • 88 is not a factor of 140 because 140 ÷ 88 = 1.59 (not an exact division).
   • 89 is not a factor of 140 because 140 ÷ 89 = 1.57 (not an exact division).
   • 90 is not a factor of 140 because 140 ÷ 90 = 1.56 (not an exact division).
   • 91 is not a factor of 140 because 140 ÷ 91 = 1.54 (not an exact division).
   • 92 is not a factor of 140 because 140 ÷ 92 = 1.52 (not an exact division).
   • 93 is not a factor of 140 because 140 ÷ 93 = 1.51 (not an exact division).
   • 94 is not a factor of 140 because 140 ÷ 94 = 1.49 (not an exact division).
   • 95 is not a factor of 140 because 140 ÷ 95 = 1.47 (not an exact division).
   • 96 is not a factor of 140 because 140 ÷ 96 = 1.46 (not an exact division).
   • 97 is not a factor of 140 because 140 ÷ 97 = 1.44 (not an exact division).
   • 98 is not a factor of 140 because 140 ÷ 98 = 1.43 (not an exact division).
   • 99 is not a factor of 140 because 140 ÷ 99 = 1.41 (not an exact division).
   • 100 is not a factor of 140 because 140 ÷ 100 = 1.4 (not an exact division).
   • 101 is not a factor of 140 because 140 ÷ 101 = 1.39 (not an exact division).
   • 102 is not a factor of 140 because 140 ÷ 102 = 1.37 (not an exact division).
   • 103 is not a factor of 140 because 140 ÷ 103 = 1.36 (not an exact division).
   • 104 is not a factor of 140 because 140 ÷ 104 = 1.35 (not an exact division).
   • 105 is not a factor of 140 because 140 ÷ 105 = 1.33 (not an exact division).
   • 106 is not a factor of 140 because 140 ÷ 106 = 1.32 (not an exact division).
   • 107 is not a factor of 140 because 140 ÷ 107 = 1.31 (not an exact division).
   • 108 is not a factor of 140 because 140 ÷ 108 = 1.3 (not an exact division).
   • 109 is not a factor of 140 because 140 ÷ 109 = 1.28 (not an exact division).
   • 110 is not a factor of 140 because 140 ÷ 110 = 1.27 (not an exact division).
   • 111 is not a factor of 140 because 140 ÷ 111 = 1.26 (not an exact division).
   • 112 is not a factor of 140 because 140 ÷ 112 = 1.25 (not an exact division).
   • 113 is not a factor of 140 because 140 ÷ 113 = 1.24 (not an exact division).
   • 114 is not a factor of 140 because 140 ÷ 114 = 1.23 (not an exact division).
   • 115 is not a factor of 140 because 140 ÷ 115 = 1.22 (not an exact division).
   • 116 is not a factor of 140 because 140 ÷ 116 = 1.21 (not an exact division).
   • 117 is not a factor of 140 because 140 ÷ 117 = 1.2 (not an exact division).
   • 118 is not a factor of 140 because 140 ÷ 118 = 1.19 (not an exact division).
   • 119 is not a factor of 140 because 140 ÷ 119 = 1.18 (not an exact division).
   • 120 is not a factor of 140 because 140 ÷ 120 = 1.17 (not an exact division).
   • 121 is not a factor of 140 because 140 ÷ 121 = 1.16 (not an exact division).
   • 122 is not a factor of 140 because 140 ÷ 122 = 1.15 (not an exact division).
   • 123 is not a factor of 140 because 140 ÷ 123 = 1.14 (not an exact division).
   • 124 is not a factor of 140 because 140 ÷ 124 = 1.13 (not an exact division).
   • 125 is not a factor of 140 because 140 ÷ 125 = 1.12 (not an exact division).
   • 126 is not a factor of 140 because 140 ÷ 126 = 1.11 (not an exact division).
   • 127 is not a factor of 140 because 140 ÷ 127 = 1.1 (not an exact division).
   • 128 is not a factor of 140 because 140 ÷ 128 = 1.09 (not an exact division).
   • 129 is not a factor of 140 because 140 ÷ 129 = 1.08 (not an exact division).
   • 130 is not a factor of 140 because 140 ÷ 130 = 1.08 (not an exact division).
   • 131 is not a factor of 140 because 140 ÷ 131 = 1.07 (not an exact division).
   • 132 is not a factor of 140 because 140 ÷ 132 = 1.06 (not an exact division).
   • 133 is not a factor of 140 because 140 ÷ 133 = 1.05 (not an exact division).
   • 134 is not a factor of 140 because 140 ÷ 134 = 1.04 (not an exact division).
   • 135 is not a factor of 140 because 140 ÷ 135 = 1.04 (not an exact division).
   • 136 is not a factor of 140 because 140 ÷ 136 = 1.03 (not an exact division).
   • 137 is not a factor of 140 because 140 ÷ 137 = 1.02 (not an exact division).
   • 138 is not a factor of 140 because 140 ÷ 138 = 1.01 (not an exact division).
   • 139 is not a factor of 140 because 140 ÷ 139 = 1.01 (not an exact division).
   • 140 is a factor of 140 because 140 ÷ 140 = 1.

3. Collecting all the numbers that are factors of 140, we get: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140.

Pair Factors and Negative Pair Factors of Factors of 140

Pair factors are pairs of numbers that, when multiplied together, give the original number. For the factors of 140, the pair factors are:

• (1, 140)
• (2, 70)
• (4, 35)
• (5, 28)
• (7, 20)
• (10, 14)

Negative pair factors are the same as pair factors, but with one of the numbers being negative. For the factors of 140, the negative pair factors are:

• (-1, -140)
• (-2, -70)
• (-4, -35)
• (-5, -28)
• (-7, -20)
• (-10, -14)

Prime Factorisation of 140

Prime factorisation is the process of expressing a number as a product of its prime factors. To find the prime factorisation of 140, we can divide it by prime numbers until we can no longer divide it further.

Dividing 140 by 2, we get 70. Dividing 70 by 2, we get 35. Dividing 35 by 5, we get 7. Since 7 is a prime number, we stop here.

Therefore, the prime factorisation of 140 is 2 × 2 × 5 × 7, or in exponential form, 2^2 × 5 × 7.

Solved Examples

1. Example: Find the factors of 140.

   Solution: The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140.

2. Example: Determine the pair factors of 140.

   Solution: The pair factors of 140 are (1, 140), (2, 70), (4, 35), (5, 28), (7, 20), and (10, 14).

3. Example: What is the prime factorisation of 140?

   Solution: The prime factorisation of 140 is 2 × 2 × 5 × 7, or 2^2 × 5 × 7.

Factors in Mathematics

In mathematics, factors are numbers that divide a given number without leaving a remainder. They play a crucial role in various mathematical concepts, such as prime factorisation, finding common factors, and solving equations.

Symbols Used to Represent Factors

In mathematics, factors are often represented using the multiplication symbol (×) or by writing the numbers next to each other. For example, the factors of 140 can be represented as 1 × 140, 2 × 70, 4 × 35, and so on.

Types of Factors

There are different types of factors, including:

1. Prime Factors: Prime factors are factors that are prime numbers. In the case of 140, the prime factors are 2, 5, and 7.

2. Pair Factors: Pair factors are pairs of numbers that, when multiplied together, give the original number. For example, the pair factors of 140 are (1, 140), (2, 70), (4, 35), and so on.

3. Negative Pair Factors: Negative pair factors are the same as pair factors, but with one of the numbers being negative. For example, the negative pair factors of 140 are (-1, -140), (-2, -70), (-4, -35), and so on.

FAQs on Factors of 140

Question: What are the factors of 140? Answer: The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140.

Question: What is the prime factorisation of 140? Answer: The prime factorisation of 140 is 2 × 2 × 5 × 7, or 2^2 × 5 × 7.

Question: What are pair factors? Answer: Pair factors are pairs of numbers that, when multiplied together, give the original number. For example, the pair factors of 140 are (1, 140), (2, 70), (4, 35), and so on.

Question: What are negative pair factors? Answer: Negative pair factors are the same as pair factors, but with one of the numbers being negative. For example, the negative pair factors of 140 are (-1, -140), (-2, -70), (-4, -35), and so on.

Question: How are factors used in mathematics? Answer: Factors are used in various mathematical concepts, such as prime factorisation, finding common factors, solving equations, and determining divisibility. They help in understanding the properties and relationships between numbers.