Factors of 56

In Maths, factorisation is the breaking up of a number into smaller numbers. The lower numbers when multiplied together give you the original number. The process of splitting a number into its factors and divisors is known as factorisation. So factors of 56 will be some prime numbers that when multiplied, give the result, as 56. This is known as prime factorisation of 56. Factors of a number are those that are evenly divisible into another number. It is of immense importance in elementary arithmetic. It can be used in many ways like determining the least common multiple or highest common factor. Typically, we factorize a number till we reach a point where it can no longer be divisible. This is generally known as prime factorization.


Definition 

When two numbers are multiplied together, and the result is a given number, then the two numbers are called factors of that particular number. For example, 5 x 3 equals 15; hence the numbers 5 and 3 are the factors of 15. The numbers that are multiplied together are called factor pairs.


What are the Factors of 56 in Pairs?

Every number is divisible by itself and one. For example, 56 /1 = 56. Since multiplication is the other side of the division, we can say that 56 x 1 = 56, so factors of 56 are 1 and 56. 1 and 56 are also known as factor pair. Similarly, there are other factors and factor pairs of the number 56, such as

7 x 8 = 56 or 56/7 = 8 and 56/8 = 7

2 x 28 = 56 or 56/2= 28

4 x 14 = 56 or 56/4=14 and 56/14 = 4.

Therefore, the factor pairs of number 56 are 1 & 56, 7 & 8, 2 & 28, and 4 & 14.


Distinct Factors

You can consider 1, 2, 4, 7, 8, 14, 28, and 56 to be distinct factors of 56. Factors and distinct factors are one and the same. Factors are positive and are evenly divisible.


However, factors can be negative also. For example, it is -56, then the factors of – 56 are

-1 x 56 or 1 x -56 = -56

-2 x 28 or 2 x -28 = -56

-7 x 8 or 7 x -8 = -56

-4 x -14 or 4 x -14 = -56


In simple words, negative factors are factors with a (-) negative sign. Similarly,

-1 x -56 = 56

-2 x -28 = 56

-7 x -8 = 56

-4 x -14 = 56


Calculation of the Factors 

Only whole numbers and integers can be converted into factors. For 56 to be an integer, you should be able to write 56 without a fraction or decimal parts, e.g. 56/3, 23/56 or 56.01. For 56 to be an integer, it has to be the whole number that is not a fraction. Thus, 56 is an integer as well as a whole number. When you divide 56 by its factors, the remainder is always a zero. For example, 


56/1 = 56, results in zero and is divided by 1

56/2 = 28, results in zero and is divided by 2

56/4 = 14, results in zero and is divided by 4  

56/7 = 8, results in zero and is divided by 8.

56/56 = 1, results in zero and is divided by 1

56/ 28 = 2, results in zero and is divided by 28   

56/8 = 7, results in zero and is divided by 8

56/14 = 4, results in zero and is divided by 14.


How to Write the Factors of 56

Let us start by writing the number 56 first. Now, we have enough knowledge about the factor and the factor pairs of 56, so let’s begin any pair. For example, 7 x 56

= 7 x 8 = 56

= 7 x 2 x 2 x 2 = 56  

Now, 7 is a prime number and it cannot break down further like the number 8. 7 can be written only as 7 x 1. So, we write the factors of 56 as = 7 x 2 x2 x 2 x 1.


Let us take another factor pair, 2 and 28

= 2 x 28 = 56  

= 2 x 14 x 2 = 56

= 2 x 7 x 2 x 2 = 56

= 2 x 2 x 2 x 7 = 56

= 2 x 2 x 2 x 7 = 56

= 2 x 2 x 2 x 7 x 1 = 56

Therefore, factors of 56 can be written as 7 x2 x 2 x 2 x 1. You will get the same answer with any other factor pair that you use. The conclusion is that the factors of number 56 are always written as 7 x2 x 2 x 2 x 1.   


Prime Factorization of 56 

Firstly, know that 56 is a composite number. You already know that 56 is a whole number as well as an integer (not a fraction and not a decimal). The multiplication can take 7 x 8 or 2 x 28, so 56 is a composite number. A composite number is made up of prime factors also. As you know, prime numbers are 1, 2, 3, 5, 7, 11, 13, 17, and 31 as they have no other factors apart from 1.


To begin with, divide the number 56 with 2, one of its prime factor.

56/2 = 28

28/2 = 14

14/2 = 7

7/2 = 3.5, a fraction. So, the next option is

7/7 = 1 

It puts a stop on further divisions. Hence, prime factors of 56 are written as 2 x 2 x 2 x 7 or 23 x 2 where 2 and 7 are the prime numbers. It is the prime factorization of 56.


Fun Facts About Factors 

1 – Factors are whole numbers, integers, and never decimals or fractions.

2 – All the even numbers always have two as a factor. 

3 – All numbers that end with five have five as a factor.

4 – All numbers ending with a zero have 2, 5 and 10 as factors.

FAQ (Frequently Asked Questions)

1 – What are the Rules of Prime Factorization?

A prime number is one which is divisible only by itself or by ‘1’. All non-prime numbers can be broken down into prime number factors (As we saw in the above case of factorisation for 56 where the factors came to 2 x 2 x 2 x 7 or 23 x 2.


Let’s take another case of ‘12’. The steps for factorisation will be

12 = 6 x 2

12 = 4 x 3

12 = 2 x 2 x 3


The last step splits the factors such that only prime numbers are left (i.e. 2 and 3). After this point, it cannot be split any further.

2 – What are the Facts About Prime Factorization?

A number that has 1 and the number itself as its factor, is called a prime number.


So, 2,3,5,7 etc are prime numbers. Once you reduce the higher numbers to all prime numbers it is called prime factorisation.


Take the case of 315

315 = 63 x 5

315 = 9 x 7 x 5

315 = 3 x 3 x 7 x 5


Prime factorization happens when we write a number as a product of all its prime factors. So prime factors of 315 are 3, 3, 7, and 5.