Factors of 120

Factors of 120

Factors of a number refer to the numbers that divide the given number without leaving a remainder. In this blog, we will explore the factors of 120 and understand their properties.

Answer to Factors of 120

The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

How to solve the problem: hints

To find the factors of 120, we can follow these steps:

1. Determine the criteria for judging whether a number is a factor. A number is a factor of 120 if it divides 120 without leaving a remainder.

2. List all the numbers starting from 1 up to the given number, which is 120 in this case.

3. Use each number as a divisor and verify whether it is a factor by dividing 120 by the number. If the division results in an integer value, then the number is a factor.

4. Finally, collect all the numbers that are factors of 120.

Let's now go through a step-by-step solution to find the factors of 120.

Step-by-step solution

1. The criteria for judging whether a number is a factor of 120 is that it should divide 120 without leaving a remainder.

2. List all the numbers starting from 1 up to 120: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, and 120.

3. Use each number as a divisor and verify whether it is a factor by dividing 120 by the number. If the division results in an integer value, then the number is a factor.

   • 120 ÷ 1 = 120 (integer result, so 1 is a factor)
   • 120 ÷ 2 = 60 (integer result, so 2 is a factor)
   • 120 ÷ 3 = 40 (integer result, so 3 is a factor)
   • 120 ÷ 4 = 30 (integer result, so 4 is a factor)
   • 120 ÷ 5 = 24 (integer result, so 5 is a factor)
   • 120 ÷ 6 = 20 (integer result, so 6 is a factor)
   • 120 ÷ 7 = 17.14 (not an integer result, so 7 is not a factor)
   • 120 ÷ 8 = 15 (integer result, so 8 is a factor)
   • 120 ÷ 9 = 13.33 (not an integer result, so 9 is not a factor)
   • 120 ÷ 10 = 12 (integer result, so 10 is a factor)
   • 120 ÷ 11 = 10.91 (not an integer result, so 11 is not a factor)
   • 120 ÷ 12 = 10 (integer result, so 12 is a factor)
   • 120 ÷ 13 = 9.23 (not an integer result, so 13 is not a factor)
   • 120 ÷ 14 = 8.57 (not an integer result, so 14 is not a factor)
   • 120 ÷ 15 = 8 (integer result, so 15 is a factor)
   • 120 ÷ 16 = 7.5 (not an integer result, so 16 is not a factor)
   • 120 ÷ 17 = 7.06 (not an integer result, so 17 is not a factor)
   • 120 ÷ 18 = 6.67 (not an integer result, so 18 is not a factor)
   • 120 ÷ 19 = 6.32 (not an integer result, so 19 is not a factor)
   • 120 ÷ 20 = 6 (integer result, so 20 is a factor)
   • 120 ÷ 21 = 5.71 (not an integer result, so 21 is not a factor)
   • 120 ÷ 22 = 5.45 (not an integer result, so 22 is not a factor)
   • 120 ÷ 23 = 5.22 (not an integer result, so 23 is not a factor)
   • 120 ÷ 24 = 5 (integer result, so 24 is a factor)
   • 120 ÷ 25 = 4.8 (not an integer result, so 25 is not a factor)
   • 120 ÷ 26 = 4.62 (not an integer result, so 26 is not a factor)
   • 120 ÷ 27 = 4.44 (not an integer result, so 27 is not a factor)
   • 120 ÷ 28 = 4.29 (not an integer result, so 28 is not a factor)
   • 120 ÷ 29 = 4.14 (not an integer result, so 29 is not a factor)
   • 120 ÷ 30 = 4 (integer result, so 30 is a factor)
   • 120 ÷ 31 = 3.87 (not an integer result, so 31 is not a factor)
   • 120 ÷ 32 = 3.75 (not an integer result, so 32 is not a factor)
   • 120 ÷ 33 = 3.64 (not an integer result, so 33 is not a factor)
   • 120 ÷ 34 = 3.53 (not an integer result, so 34 is not a factor)
   • 120 ÷ 35 = 3.43 (not an integer result, so 35 is not a factor)
   • 120 ÷ 36 = 3.33 (not an integer result, so 36 is not a factor)
   • 120 ÷ 37 = 3.24 (not an integer result, so 37 is not a factor)
   • 120 ÷ 38 = 3.16 (not an integer result, so 38 is not a factor)
   • 120 ÷ 39 = 3.08 (not an integer result, so 39 is not a factor)
   • 120 ÷ 40 = 3 (integer result, so 40 is a factor)
   • 120 ÷ 41 = 2.93 (not an integer result, so 41 is not a factor)
   • 120 ÷ 42 = 2.86 (not an integer result, so 42 is not a factor)
   • 120 ÷ 43 = 2.79 (not an integer result, so 43 is not a factor)
   • 120 ÷ 44 = 2.73 (not an integer result, so 44 is not a factor)
   • 120 ÷ 45 = 2.67 (not an integer result, so 45 is not a factor)
   • 120 ÷ 46 = 2.61 (not an integer result, so 46 is not a factor)
   • 120 ÷ 47 = 2.55 (not an integer result, so 47 is not a factor)
   • 120 ÷ 48 = 2.5 (not an integer result, so 48 is not a factor)
   • 120 ÷ 49 = 2.45 (not an integer result, so 49 is not a factor)
   • 120 ÷ 50 = 2.4 (not an integer result, so 50 is not a factor)
   • 120 ÷ 51 = 2.35 (not an integer result, so 51 is not a factor)
   • 120 ÷ 52 = 2.31 (not an integer result, so 52 is not a factor)
   • 120 ÷ 53 = 2.26 (not an integer result, so 53 is not a factor)
   • 120 ÷ 54 = 2.22 (not an integer result, so 54 is not a factor)
   • 120 ÷ 55 = 2.18 (not an integer result, so 55 is not a factor)
   • 120 ÷ 56 = 2.14 (not an integer result, so 56 is not a factor)
   • 120 ÷ 57 = 2.11 (not an integer result, so 57 is not a factor)
   • 120 ÷ 58 = 2.07 (not an integer result, so 58 is not a factor)
   • 120 ÷ 59 = 2.03 (not an integer result, so 59 is not a factor)
   • 120 ÷ 60 = 2 (integer result, so 60 is a factor)
   • 120 ÷ 61 = 1.97 (not an integer result, so 61 is not a factor)
   • 120 ÷ 62 = 1.94 (not an integer result, so 62 is not a factor)
   • 120 ÷ 63 = 1.9 (not an integer result, so 63 is not a factor)
   • 120 ÷ 64 = 1.88 (not an integer result, so 64 is not a factor)
   • 120 ÷ 65 = 1.85 (not an integer result, so 65 is not a factor)
   • 120 ÷ 66 = 1.82 (not an integer result, so 66 is not a factor)
   • 120 ÷ 67 = 1.79 (not an integer result, so 67 is not a factor)
   • 120 ÷ 68 = 1.76 (not an integer result, so 68 is not a factor)
   • 120 ÷ 69 = 1.74 (not an integer result, so 69 is not a factor)
   • 120 ÷ 70 = 1.71 (not an integer result, so 70 is not a factor)
   • 120 ÷ 71 = 1.69 (not an integer result, so 71 is not a factor)
   • 120 ÷ 72 = 1.67 (not an integer result, so 72 is not a factor)
   • 120 ÷ 73 = 1.64 (not an integer result, so 73 is not a factor)
   • 120 ÷ 74 = 1.62 (not an integer result, so 74 is not a factor)
   • 120 ÷ 75 = 1.6 (not an integer result, so 75 is not a factor)
   • 120 ÷ 76 = 1.58 (not an integer result, so 76 is not a factor)
   • 120 ÷ 77 = 1.56 (not an integer result, so 77 is not a factor)
   • 120 ÷ 78 = 1.54 (not an integer result, so 78 is not a factor)
   • 120 ÷ 79 = 1.52 (not an integer result, so 79 is not a factor)
   • 120 ÷ 80 = 1.5 (not an integer result, so 80 is not a factor)
   • 120 ÷ 81 = 1.48 (not an integer result, so 81 is not a factor)
   • 120 ÷ 82 = 1.46 (not an integer result, so 82 is not a factor)
   • 120 ÷ 83 = 1.45 (not an integer result, so 83 is not a factor)
   • 120 ÷ 84 = 1.43 (not an integer result, so 84 is not a factor)
   • 120 ÷ 85 = 1.41 (not an integer result, so 85 is not a factor)
   • 120 ÷ 86 = 1.4 (not an integer result, so 86 is not a factor)
   • 120 ÷ 87 = 1.38 (not an integer result, so 87 is not a factor)
   • 120 ÷ 88 = 1.36 (not an integer result, so 88 is not a factor)
   • 120 ÷ 89 = 1.35 (not an integer result, so 89 is not a factor)
   • 120 ÷ 90 = 1.33 (not an integer result, so 90 is not a factor)
   • 120 ÷ 91 = 1.32 (not an integer result, so 91 is not a factor)
   • 120 ÷ 92 = 1.3 (not an integer result, so 92 is not a factor)
   • 120 ÷ 93 = 1.29 (not an integer result, so 93 is not a factor)
   • 120 ÷ 94 = 1.28 (not an integer result, so 94 is not a factor)
   • 120 ÷ 95 = 1.26 (not an integer result, so 95 is not a factor)
   • 120 ÷ 96 = 1.25 (not an integer result, so 96 is not a factor)
   • 120 ÷ 97 = 1.24 (not an integer result, so 97 is not a factor)
   • 120 ÷ 98 = 1.22 (not an integer result, so 98 is not a factor)
   • 120 ÷ 99 = 1.21 (not an integer result, so 99 is not a factor)
   • 120 ÷ 100 = 1.2 (not an integer result, so 100 is not a factor)
   • 120 ÷ 101 = 1.19 (not an integer result, so 101 is not a factor)
   • 120 ÷ 102 = 1.18 (not an integer result, so 102 is not a factor)
   • 120 ÷ 103 = 1.17 (not an integer result, so 103 is not a factor)
   • 120 ÷ 104 = 1.15 (not an integer result, so 104 is not a factor)
   • 120 ÷ 105 = 1.14 (not an integer result, so 105 is not a factor)
   • 120 ÷ 106 = 1.13 (not an integer result, so 106 is not a factor)
   • 120 ÷ 107 = 1.12 (not an integer result, so 107 is not a factor)
   • 120 ÷ 108 = 1.11 (not an integer result, so 108 is not a factor)
   • 120 ÷ 109 = 1.1 (not an integer result, so 109 is not a factor)
   • 120 ÷ 110 = 1.09 (not an integer result, so 110 is not a factor)
   • 120 ÷ 111 = 1.08 (not an integer result, so 111 is not a factor)
   • 120 ÷ 112 = 1.07 (not an integer result, so 112 is not a factor)
   • 120 ÷ 113 = 1.06 (not an integer result, so 113 is not a factor)
   • 120 ÷ 114 = 1.05 (not an integer result, so 114 is not a factor)
   • 120 ÷ 115 = 1.04 (not an integer result, so 115 is not a factor)
   • 120 ÷ 116 = 1.03 (not an integer result, so 116 is not a factor)
   • 120 ÷ 117 = 1.03 (not an integer result, so 117 is not a factor)
   • 120 ÷ 118 = 1.02 (not an integer result, so 118 is not a factor)
   • 120 ÷ 119 = 1.01 (not an integer result, so 119 is not a factor)
   • 120 ÷ 120 = 1 (integer result, so 120 is a factor)

4. Finally, we collect all the numbers that are factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Pair Factors and Negative Pair Factors of Factors of 120

The pair factors of 120 are the pairs of numbers that multiply together to give 120. For example, the pair factors of 120 are (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), and (10, 12).

The negative pair factors of 120 are the pairs of numbers that multiply together to give -120. Since -120 is the negative of 120, the negative pair factors are the same as the positive pair factors, but with one number being negative. For example, the negative pair factors of 120 are (-1, -120), (-2, -60), (-3, -40), (-4, -30), (-5, -24), (-6, -20), (-8, -15), and (-10, -12).

Prime Factorisation of 120

Prime factorisation of a number involves expressing the number as a product of its prime factors. To find the prime factorisation of 120, we divide it by prime numbers until we can no longer divide it further.

The prime factorisation of 120 is 2^3 × 3 × 5. This means that 120 can be expressed as the product of 2 raised to the power of 3, multiplied by 3, and multiplied by 5.

Solved Examples

1. Example: Find the factors of 120.

   Solution: The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

2. Example: Find the pair factors of 120.

   Solution: The pair factors of 120 are (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), and (10, 12).

3. Example: Find the prime factorisation of 120.

   Solution: The prime factorisation of 120 is 2^3 × 3 × 5.

Factors in Mathematics

In mathematics, factors are numbers that divide a given number without leaving a remainder. They are the divisors of a number and 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 a dot (·). For example, the factors of 120 can be represented as 1 × 120, 2 × 60, 3 × 40, and so on.

Types of Factors

There are different types of factors based on their properties:

1. Prime Factors: Prime factors are the factors that are prime numbers. They cannot be further divided into smaller factors.

2. Composite Factors: Composite factors are the factors that are composite numbers. They can be further divided into smaller factors.

3. Pair Factors: Pair factors are the pairs of numbers that multiply together to give the original number.

4. Negative Pair Factors: Negative pair factors are the pairs of numbers that multiply together to give the negative of the original number.

FAQs on Factors of 120

Question: What are the factors of 120? Answer: The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Question: What is the prime factorisation of 120? Answer: The prime factorisation of 120 is 2^3 × 3 × 5.

Question: What are pair factors? Answer: Pair factors are the pairs of numbers that multiply together to give a specific number. For example, the pair factors of 120 are (1, 120), (2, 60), (3, 40), and so on.

Question: What are negative pair factors? Answer: Negative pair factors are the pairs of numbers that multiply together to give the negative of a specific number. For example, the negative pair factors of 120 are (-1, -120), (-2, -60), (-3, -40), 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.