Factors of 70 | with Easy division and prime factorization

Factors of 70

There are seven factors of 70, which divide by 70 exactly without leaving a remainder. 

It is possible for the factors and pair factors of 70 to be positive or negative.

For example, 70 must have a pair factor (1, 70) or (-1, -70). The original number 70 will result from multiplying a pair of negative numbers, such as multiplying -1 and -70.

Using the prime factorization method, I will discuss the factors of 70, pair factors, and prime factors of 70.

What are the Factors of 70?

Factors of 70 are the numbers dividing 70 exactly without leaving a remainder. 70 is an even composite number, which means it has many factors besides 1 and 70. 

Hence, 

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

Similarly,

Negative factors of 70= -1, -2, -5, -7, -10, -14, -35, and -70.

Prime Factorization of 70: 2 × 5 × 7

What are the Factors of -70?

When we multiply two numbers, and we get -70 as a product, those numbers are the factors of -70. 

Here is the explanation:

-1 × 70 = -70 

1 × -70 = -70

-2 × 35 = -70

 2 × -35 = -70

-5 × 14 = -70

5  × -14 = -70

-7 × 10 = -70

7 × -10 = -70

We can get -70 by having (-1, 70), (-2, 35), (-5, 14), and (-7, 10) as a pair of factors. Similarly, we can also get -70 by having (1, -70), (2, -35), (5, -14), and (7, -10) as a pair of factors.

Pair Factors of 70

You can find the pair factors of 70 by multiplying two numbers in a pair to arrive at the original number. Certain numbers are listed below.

Positive Pair Factors of 70:

Therefore, 70 has four positive pair factors: (1, 70), (2, 35), (5, 14), and (7, 10).

Negative Pair Factors of 70:

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

How to calculate the Prime Factors of 70?

The factors of 70 can be calculated by following the steps below.

• Write the number 70 first.
• Find the two numbers, such as 2 and 35, that give a result of 70 when multiplied. 

For example, 2 + 35 = 70.

• The only factors of the prime number 2 are 1 and the number itself (1 and 2 ) and they cannot be factorized further.

2 = 2 × 1

• Here’s another example: 35 is a composite number, not a prime number, and can be factored further. Therefore, 35 can be factored as 5 × 7 × 1
• Thus, the factorization of 70 is 7 × 5 × 2 × 1
• As a final step, write down all the unique factors.

Prime Factorization of 70

As a composite number, 70 should have prime factors. Let’s find out how to find 70’s prime factors.

Step 1: Start by dividing 70 by the smallest prime factor that you can think of, like 2.

70 ÷ 2 = 35

Step 2: Now divide 35 by 2 and 3 again, you will get a fractional value and you can move on to the next prime number, say 5.

35 ÷ 5 = 7

Step 3: If you divide 7 by 5, you’ll get a fraction. Move on to the next prime factor, 7.

7 ÷ 7 = 1

We received the number 1 at the end of the division process. As a result, we cannot continue. Thus, the prime factors of 70 are written as 2, 5, and 10, where 2, 5, and 10 are prime numbers.

With the help of prime factorization, you can find the exact number of factors of the number 70. 2, 5, and 7 are the prime factors of 70. There are three exponents in the prime factorization: 1, 1, and 1. Add those numbers together and multiply them.

 (1+1)(1+1)(1+1) = 2 x 2 x 2= 8. 

Thus, there are 8 factors in the number 70.

Solved Examples

Example 1:

Calculate the common factors of 16 and 39.

Solution:

Factors of 16: 1, 2, 4, 8, and 16.

The factors of 39 is 1, 3, 13, and 39.

Therefore, 70 and 69 have a common factor of 1.

Example 2:

Calculate the common factors of 70 and 24.

Solution:

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

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.

As 71 is a prime number, the common factor of 70 and 24 is 1, and 2 only.

Example 3:

Calculate the common factor of 70 and 8.

Solution:

There are 11 factors of 70: 1, 2, 5, 7, 10, 14, 35, and 70.

Factors of 8 are 1, 2, 4, and 8.

As a result, 70 and 8 have 1, 2 common factors.

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