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Express 56 as the product of its prime factors?

Before finding the prime factors of 56 we must know what the term ‘factors’ mean. When two numbers are multiplied together, and the result is a given number, then the two numbers are called factors of that number. 

Factors of 56 are all such numbers that completely divides the number 56 and when multiplied in pairs give the product as 56. 

These factors of 56 are positive numbers but can be negative as well. 

All such numbers that divide 56 without any remainder are factors of 56. Only whole numbers and integers can be the factors of a number.  

So, the factors of 56 are 1 , 2 , 4 , 7 , 8 , 14 , 28  and 56. This means that all these numbers divide 56 completely.  

 Important points to remember 

  • Decimals and fractions (anything that is not integer) cannot be the factors of any number.  
  • When a number is a factor of the given number, then its additive inverse is also a factor of the given number. For example, since 4 is a factor of 56, – 4 is also a factor of 56.  

Now, before finding the prime factors of 56 we must know what we mean by prime numbers. 

Prime numbers are the basic building blocks of all the numbers. They can’t be divided by any number apart from 1 or themselves.  

That means a prime number is a number that has exactly two factors, 1 and the number itself.   

Prime factorization means to represent any given number as a product of prime numbers. 

There are various methods for finding the prime factors of a number.  

  • Division method 
  • Factor tree method  
  • Division method  

 Prime Factorization of 56 by division method  

We know that 56 is a composite number and it will be having factors that can be further broken into prime numbers. Now let us know how to find out the prime factors of 56.  

Step 1:  Let’s divide the number 56 with the smallest prime number i.e. 2  

Therefore, 56 / 2 = 28 

Step2:  Again, divide 28 by 2 and the process goes on.  

 28 / 2 = 14 

  14 / 2  = 7  

Step 3: Now, if we divide 7 by 2 we will get a fractional number, which cannot be a factor. So, we move to next prime number that divides 7 completely which is 7 itself.  

   7  /  7  =   1  

Step 4:  We have received 1 at the end of the division process and so that we cannot proceed further.  

So, the prime factors of 56 are 2  x 2 x 2 x 7  

56 as the product of its prime factors by division method = 2 x 2 x 2 x 7 where 2 and 7 both are prime numbers.  

Prime Factorization  

It is just like the division method. The only difference is that presentation. 

2  56 
2  28 
2  14 
7  7 


So, prime factorization becomes 56 = 2 * 2 * 2 * 7. 

Prime Factorization of 56 by Factor Tree Method  

Prime factors of 56 can also be found by making a factor tree. Here, we need to count the last most nodes or leaves of the tree.  

Thus, the prime factors of 56 are 2 x 2 x 2 x 7   by factor tree.  

From the above two methods we can conclude that 56 as the product of its prime factors = 2 x 2 x 2 x 7 . 

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