Factors of 56: Pair factors and Prime Factors – Mindspark

What are The Factors of 56?

The numbers that divide 56 completely are called its factors. That’s why 1, 2, 4, 7, 8, 14, 28, and 56 are the required factors as per the definition.

In other words, if two whole numbers are multiplied with each other, and the result is 56, then both the whole numbers are factors of 56.

For example,

1 × 56 = 56

2 × 28 = 56

4 × 14 = 56

7 × 8 = 56

so 1, 2, 4, 7, 8, 14, 28, and 56 are the required factors.

How To Calculate the Factors of The Number 56?

The numbers that divide 56 completely without leaving any remainder are its factors. Every number is completely divisible by 1 and the number itself. So, the two factors will be 1 and the number itself, which is 56. 

To find other factors, we will use the divisibility test.

Using the divisibility rules from 1 to 10, we find that 56 is divisible by 2, 4, 7, and 8. By dividing 56 with these numbers, we can find other factors.

So, divide 56 with 2; we get (56 ÷ 2) = 28 as the quotient and zero as the remainder.

Since the quotient is 28 and the remainder is 0. So, 56 will be wholly divisible by the quotient 28 also. Therefore, 28 is also a factor of 56.

Similarly, when we divide 56 by 4 and 7, we get 14 and 8, respectively. All these numbers are the required factors.

Therefore, we see that all the factors of the number 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

Pair Factors of 56

To find the pair factors, we will have to find pairs of such numbers whose product is 56. These pairs are – 

1 × 56 = 56

2 × 28 = 56

4 × 14 = 56

7 × 8 = 56

Hence, the positive pair factors are (1, 56), (2, 28), (4, 14), and (7, 8).

In the same way, (-1, -56), (-2, -28), (-4, -14), and (-7, -8) will be its negative pair factors.  It is because the product of two negative numbers is a positive number.

Prime Factorization of 56

To find the prime factors, we will have to divide 56 by prime numbers till the quotient obtained is 1. Let’s understand how to do it. 

The smallest prime factor of 56 is 2. So divide 56 by 2, and we get;

            \frac{56}{2}=28

The smallest prime factor of 28 is also 2. Now divide 28 by 2, and we get;

            \frac{28}{2}=14

Similarly, divide 14 by 2, and we get 7. 

Finally, divide 7 by 7, and we get 1.

Now, we can’t divide 1 by any further by prime factors. 

Therefore, prime factorization of 56 is equal to (2\times 2\times 2\times 7)\text{ or }\left(2^{3} \times 7\right).

Examples

1. Identify the factors of 56 among the following numbers – 

8, 12, 14, 18?

8 and 14 are the factors of 56 since these two numbers divide 56 completely without leaving any remainder.

2. What is the sum of all the factors of the number 56?

1, 2, 4, 7, 8, 14, 28, and 56 are the factors of the number 56.

So, the sum of these factors = 1 + 2 + 4 + 7 + 8 + 14 + 28 + 56 = 120

Therefore, 120 is the required answer.