The factors of 70 are the numbers that divide 70 exactly without leaving a remainder. The factors and the pair factors of 70 can be positive or negative. For example, the pair factor of 70 can be (1, 70) or(-1, -70). If we multiply a pair of negative numbers, such as multiplying -1 and -70, it will result in the original number 70. In this article, we are going to discuss the factors of 70, pair factors and the prime factors of 70 using the prime factorization method and many solved examples.

Table of Contents:

• What are the Factors of 70?
• Pair Factors of 70
• How to Find the Prime Factors of 70?
• Prime Factorization of 70
• Solved Examples
• FAQs

What are the Factors of 70?

The numbers that divide 70 exactly without leaving a remainder are the factors of 70. As 70 is an even composite number, it has many factors other than 1 and 70. Hence, the factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. Similarly, the negative factors of 70 are -1, -2, -5, -7, -10, -14, -35, and -70.

Pair Factors of 70

To find the pair factors of 70, multiply the two numbers in a pair to get the original number as 70, such numbers are as follows

Positive Pair Factors of 70:

Therefore, the positive pair factors of 70 are (1, 70), (2, 35), (5, 14), and (7, 10).

Negative Pair Factors of 70:

Therefore, the negative pair factors of 70 are (-1, -70), (-2, -35), (-5, -14) and (-7, -10).

How to calculate the Prime Factors of 70?

Learn the following steps to calculate the factors of 70.

• • First, write the number 70
  • Find the two numbers, which gives the result as 70 under the multiplication, say 2 and 35, such as 2 × 35 = 70.
  • We know that 2 is a prime number that has only two factors, i.e., 1 and the number itself (1 and 2) which cannot be further factorized. (i.e) 2 = 2 × 1

• • But look at the number 35, which is a composite number but not a prime number and it can be further factorized. Thus, 35 can be factored as 5 x 7 x 1
  • Therefore, the factorization of 70 is written as 70 = 7 x 5 x 2 x 1
  • Finally, write down all the unique numbers that are obtained as factors.

Prime Factorization of 70

The number 70 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 70.

Step 1: The first step is to divide the number 70 with the smallest prime factor, say 2.

70 ÷ 2 = 35

Step 2: Again if you divide 35 by 2 and 3, you will get a fractional value and proceed with the next prime number say 5.

35 ÷ 5 = 7

Step 3: You will get a fractional number if you divide 7 by 5. So, continue with the next prime factor, 7

7 ÷ 7 = 1

At the end of the division process, we received the number 1. So that we cannot proceed further. So, the prime factors of 70 are written as 2 x 5 x 7, where 2, 5 and 7 are the prime numbers.

It is possible to find the exact number of factors of a number 70 with the help of prime factorisation. The prime factor of the 70 is 2 x 5 x 7. The exponents in the prime factorisation are 1, 1 and 1. Add the number 1 with the exponents and multiply it. (1+1)(1+1)(1+1) = 2 x 2 x 2= 8. Therefore, the number 70 has 8 factors.

Examples

Example 1:

Find the common factors of 70 and 69.

Solution:

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

The factors of 69 are 1, 3, 23 and 69.

Thus, the common factor of 70 and 69 is 1.

Example 2:

Find the common factors of 70 and 71.

Solution:

Factors of 70 = 1, 2, 5, 7, 10, 14, 35, and 70.

Factors of 71 = 1 and 71.

As 71 is a prime number, the common factor of 70 and 71 is 1 only.

Example 3:

Find the common factors of 70 and 35.

Solution:

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

The factors of 35  are 1, 5, 7 and 35.

Hence, the common factors of 70 and 35 are 1, 5, 7 and 35.

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