Factors Of 56 – With Division and Prime Factorization

factors of 56

Factors Of 56

The factors of 56 are the numbers that can be multiplied together to produce the number 56. There are no fractions or decimals associated with the number 56, so its factor pairs are those whole numbers that are either positive or negative. 

Consider, for example, the factor pair 56, written as (1, 56) and (-1, -56). From these examples, we can see that we can consider both positive and negative factor pairs of 56. We will use the factorization method to find the factors of a number, 56. 

This article will learn the factors of 56, pair factors, and the prime factors of 56 using the prime factorization method with many solved examples.

What are the Factors of 56?

The factors of 56 are the numbers that divide 56 exactly. Thus, every number that results in 56 when multiplied in pairs is one of the factors of 56. It has many factors other than 1 and 56 since 56 is an even composite number. Therefore, 56 has 1, 2, 4, 7, 8, 14, 28, and 56.

Factors of 56: 1, 2, 4, 7, 8, 14, 28 and 56.

Prime Factorization of 56: 2×2×2×7 or 23 × 7.

factors of 56

What are the Factors of -56?

Factors of -56: -1, -2, -4, -7, -8, -14, -28 and -56.

By multiplying two numbers to get the product -56, we get:

-1 x  56 =  -56    &   1 x -56 =  -56

-2 x  28 = -56     &  2 x  -28 = -56

-4 x  14 = -56     &  4 x  -14 = -56

-7 x  8 = -56    &  7 x  -8 = -56

Pair Factors of 56

You can find the pair factors by multiplying two numbers in a pair to get the original number 56, which are as follows:

Positive pair FactorsNegative Pair Factors
1 × 56 = 56 ⇒(1, 56)-1 × -56 = 56 ⇒(-1, -56)
2 × 28 = 56 ⇒ (2, 28)-2 × -28 = 56 ⇒ (-2, -28)
4 × 14 = 56 ⇒ (4, 14)-4 × -14 = 56 ⇒ (-4, -14)
7 × 8 = 56 ⇒(7, 8)-7 × -8 = 56 ⇒(-7, -8)

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

Furthermore, the negative pair factors of 56 are (-1, -56), (-2, -28), (-4, -14) and (-7, -8).

factors of 56 in pairs

Factors of 56 by Division Method

To find the factors of 56, divide it by consecutive integers in the division method. Integers that divide 56 exactly are factors of 56. We’ll start by dividing 56 by 1 and continue with other integer numbers.

  • 56/1 = 56 
  • 56/2 = 28 
  • 56/4 = 14 
  • 56/7 = 8 
  • 56/8 = 7
  • 56/14 = 4 
  • 56/28 = 2 
  • 56/56 = 1 

As a result, 56 comprises the factors 1, 2, 4, 7, 8, 14, 28, and 56.

Note:

By dividing 56 by numbers other than 1, 2, 4, 7, 8, 14, 28, and 56, a remainder is left behind, so they are not the factors of 56.

factors of 56 by division

Prime Factorization of 56

It has prime factors, which makes it a composite number. The next step is to find the prime factors of a number.

  • To divide 56, choose the smallest prime factor, say 2.

            56 ÷ 2 = 28

  • Divide 28 by 2 again and repeat the process.

            28 ÷ 2 = 14

            14 ÷ 2 = 7

  • We get a fraction if we divide 7 by 2, which can’t be a factor. Let’s move on to the next prime number, which is 7.
  •   7 ÷ 7 = 1
  • In the division process, we received 1, so we cannot proceed. 

Therefore, the prime factors are 2 × 2 × 2 × 7 or 23 × 7, where 2 and 7 are the prime numbers.

Examples

Example 1:

Find the common factor between 56 and 57.

Solution:

Factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56 

1, 3, 19, and 57 are the factors of 57.

Therefore, 56 and 57 have a common factor of 1.

Example 2:

Calculate the common factors between 56 and 55.

Solution:

In this equation, 56 = 1, 2, 4, 7, 8, 14, 28 and 56

The factors of 55 are 1, 5, 11 and 55.

Therefore, 56 and 55 have a common factor of 1.

Example 3:

Find 56 and 65’s common factors.

Solution:

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

65 has the factors 1, 5, 13, and 65.

Therefore, the common factor between 56 and 65 is only 1.

FAQs

Can you explain the 56 Factors?

An original number of 56 is obtained by multiplying a pair of numbers. It is called the factors of 56. Thus, 56 has 1, 2, 4, 7, 8, 14, 28, and 56.

The prime factorization of 56 is?

Prime factorization of 56 is 2×2×2×7 or 23 × 7

How many positive pair factors does 56 have?

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

What are the negative pair factors for 56?

56 has negative pair factors of (-1, -56), (-2, -28), (-4, -14) and (-7, -8).

14 is a factor of 56, right?

Right, 14 is a factor of 56. By dividing 56 by 14, we get 0 as the remainder, so 14 is a factor of 56.

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