Factors of 70

Factors of 70

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 70 and understand their properties.

Answer to Factors of 70

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

How to solve the problem: hints

To find the factors of 70, we can follow these steps:

1. Determine the criteria for judging whether a number is a factor. A number is a factor of 70 if it divides 70 without leaving a remainder.

2. List all the numbers starting from 1 up to the given number, which is 70 in this case.

3. Use each number as a divisor and verify whether it is a factor by dividing 70 by the number. If the division results in an integer value, then the number is a factor of 70.

4. Finally, collect all the numbers that are factors of 70.

Let's now go through a step-by-step solution to find the factors of 70.

Step-by-step solution

1. We start by listing all the numbers from 1 to 70: 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.

2. Now, we divide 70 by each number and check if the division results in an integer value.

   • 70 ÷ 1 = 70 (integer value, so 1 is a factor)
   • 70 ÷ 2 = 35 (integer value, so 2 is a factor)
   • 70 ÷ 3 = 23.33 (not an integer value, so 3 is not a factor)
   • 70 ÷ 4 = 17.5 (not an integer value, so 4 is not a factor)
   • 70 ÷ 5 = 14 (integer value, so 5 is a factor)
   • 70 ÷ 6 = 11.67 (not an integer value, so 6 is not a factor)
   • 70 ÷ 7 = 10 (integer value, so 7 is a factor)
   • 70 ÷ 8 = 8.75 (not an integer value, so 8 is not a factor)
   • 70 ÷ 9 = 7.78 (not an integer value, so 9 is not a factor)
   • 70 ÷ 10 = 7 (integer value, so 10 is a factor)
   • 70 ÷ 11 = 6.36 (not an integer value, so 11 is not a factor)
   • 70 ÷ 12 = 5.83 (not an integer value, so 12 is not a factor)
   • 70 ÷ 13 = 5.38 (not an integer value, so 13 is not a factor)
   • 70 ÷ 14 = 5 (integer value, so 14 is a factor)
   • 70 ÷ 15 = 4.67 (not an integer value, so 15 is not a factor)
   • 70 ÷ 16 = 4.38 (not an integer value, so 16 is not a factor)
   • 70 ÷ 17 = 4.12 (not an integer value, so 17 is not a factor)
   • 70 ÷ 18 = 3.89 (not an integer value, so 18 is not a factor)
   • 70 ÷ 19 = 3.68 (not an integer value, so 19 is not a factor)
   • 70 ÷ 20 = 3.5 (not an integer value, so 20 is not a factor)
   • 70 ÷ 21 = 3.33 (not an integer value, so 21 is not a factor)
   • 70 ÷ 22 = 3.18 (not an integer value, so 22 is not a factor)
   • 70 ÷ 23 = 3.04 (not an integer value, so 23 is not a factor)
   • 70 ÷ 24 = 2.92 (not an integer value, so 24 is not a factor)
   • 70 ÷ 25 = 2.8 (not an integer value, so 25 is not a factor)
   • 70 ÷ 26 = 2.69 (not an integer value, so 26 is not a factor)
   • 70 ÷ 27 = 2.59 (not an integer value, so 27 is not a factor)
   • 70 ÷ 28 = 2.5 (not an integer value, so 28 is not a factor)
   • 70 ÷ 29 = 2.41 (not an integer value, so 29 is not a factor)
   • 70 ÷ 30 = 2.33 (not an integer value, so 30 is not a factor)
   • 70 ÷ 31 = 2.26 (not an integer value, so 31 is not a factor)
   • 70 ÷ 32 = 2.19 (not an integer value, so 32 is not a factor)
   • 70 ÷ 33 = 2.12 (not an integer value, so 33 is not a factor)
   • 70 ÷ 34 = 2.06 (not an integer value, so 34 is not a factor)
   • 70 ÷ 35 = 2 (integer value, so 35 is a factor)
   • 70 ÷ 36 = 1.94 (not an integer value, so 36 is not a factor)
   • 70 ÷ 37 = 1.89 (not an integer value, so 37 is not a factor)
   • 70 ÷ 38 = 1.84 (not an integer value, so 38 is not a factor)
   • 70 ÷ 39 = 1.79 (not an integer value, so 39 is not a factor)
   • 70 ÷ 40 = 1.75 (not an integer value, so 40 is not a factor)
   • 70 ÷ 41 = 1.71 (not an integer value, so 41 is not a factor)
   • 70 ÷ 42 = 1.67 (not an integer value, so 42 is not a factor)
   • 70 ÷ 43 = 1.63 (not an integer value, so 43 is not a factor)
   • 70 ÷ 44 = 1.59 (not an integer value, so 44 is not a factor)
   • 70 ÷ 45 = 1.56 (not an integer value, so 45 is not a factor)
   • 70 ÷ 46 = 1.52 (not an integer value, so 46 is not a factor)
   • 70 ÷ 47 = 1.49 (not an integer value, so 47 is not a factor)
   • 70 ÷ 48 = 1.46 (not an integer value, so 48 is not a factor)
   • 70 ÷ 49 = 1.43 (not an integer value, so 49 is not a factor)
   • 70 ÷ 50 = 1.4 (not an integer value, so 50 is not a factor)
   • 70 ÷ 51 = 1.37 (not an integer value, so 51 is not a factor)
   • 70 ÷ 52 = 1.35 (not an integer value, so 52 is not a factor)
   • 70 ÷ 53 = 1.32 (not an integer value, so 53 is not a factor)
   • 70 ÷ 54 = 1.3 (not an integer value, so 54 is not a factor)
   • 70 ÷ 55 = 1.27 (not an integer value, so 55 is not a factor)
   • 70 ÷ 56 = 1.25 (not an integer value, so 56 is not a factor)
   • 70 ÷ 57 = 1.23 (not an integer value, so 57 is not a factor)
   • 70 ÷ 58 = 1.21 (not an integer value, so 58 is not a factor)
   • 70 ÷ 59 = 1.19 (not an integer value, so 59 is not a factor)
   • 70 ÷ 60 = 1.17 (not an integer value, so 60 is not a factor)
   • 70 ÷ 61 = 1.15 (not an integer value, so 61 is not a factor)
   • 70 ÷ 62 = 1.13 (not an integer value, so 62 is not a factor)
   • 70 ÷ 63 = 1.11 (not an integer value, so 63 is not a factor)
   • 70 ÷ 64 = 1.09 (not an integer value, so 64 is not a factor)
   • 70 ÷ 65 = 1.08 (not an integer value, so 65 is not a factor)
   • 70 ÷ 66 = 1.06 (not an integer value, so 66 is not a factor)
   • 70 ÷ 67 = 1.04 (not an integer value, so 67 is not a factor)
   • 70 ÷ 68 = 1.03 (not an integer value, so 68 is not a factor)
   • 70 ÷ 69 = 1.01 (not an integer value, so 69 is not a factor)
   • 70 ÷ 70 = 1 (integer value, so 70 is a factor)

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

Pair Factors and Negative Pair Factors of Factors of 70

Pair factors of a number are the factors that can be multiplied together to give the original number. For example, the pair factors of 70 are (1, 70), (2, 35), (5, 14), and (7, 10).

Negative pair factors are the pair factors where one factor is negative and the other is positive. For example, the negative pair factors of 70 are (-1, -70), (-2, -35), (-5, -14), and (-7, -10).

Prime Factorisation of 70

Prime factorisation of a number involves expressing the number as a product of its prime factors. The prime factors of 70 are 2, 5, and 7. Therefore, the prime factorisation of 70 is 2 × 5 × 7.

Solved Examples

1. Example: Find the factors of 70.

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

2. Example: Determine the pair factors of 70.

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

3. Example: What is the prime factorisation of 70?

   Solution: The prime factorisation of 70 is 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

The symbol ":" or "|" is commonly used to represent factors. For example, we can write "2:70" or "2|70" to represent that 2 is a factor of 70.

Types of Factors

There are two types of factors: prime factors and composite factors.

• Prime factors are the factors that are prime numbers. In the case of 70, the prime factors are 2, 5, and 7.

• Composite factors are the factors that are composite numbers, i.e., they have more than two factors. In the case of 70, all the factors except 1, 2, 5, and 7 are composite factors.

FAQs on Factors of 70

Question: What are the factors of 70?

Answer: The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

Question: What is the prime factorisation of 70?

Answer: The prime factorisation of 70 is 2 × 5 × 7.

Question: How many factors does 70 have?

Answer: 70 has a total of 8 factors.

Question: What are the pair factors of 70?

Answer: The pair factors of 70 are (1, 70), (2, 35), (5, 14), and (7, 10).

Question: Are negative numbers factors of 70?

Answer: Yes, negative numbers can also be factors of 70. For example, -1, -2, -5, -7, -10, -14, -35, and -70 are all factors of 70.

In conclusion, the factors of 70 are the numbers that divide 70 without leaving a remainder. They play a significant role in various mathematical concepts and calculations. By understanding the factors of a number, we can solve problems related to divisibility, prime factorisation, and finding common factors.