Question

How do you write the prime factorization of 28?

Answer 1

Hint:
The prime factorization can be done in two methods. One is by long division method and other is by factor tree. One can follow one of the two methods to find the prime factorization of any number.

Complete Step by Step Solution:
The objective of the problem is to find the prime factorisation of 28.
To solve this we use two methods of prime factorization. The two methods are long division method and factor tree.
Method 1: prime factorization by long division method
For this first we divide the number by the smallest prime number which is exactly divisible.
Again we divide the obtained quotient by the same or another smallest prime number. Repeat the process until quotient becomes one.
The prime factors are 2,3,5,7,11,13,17,19,23,29 and so on.
The least prime factor is 2. So divide the number by 2
$
  2\left| \!{\underline {\,
  {28} \,}} \right. \\
  2\left| \!{\underline {\,
  {14} \,}} \right. \\
  7\left| \!{\underline {\,
  7 \,}} \right. \\
  \,\,\,1 \\
 $
The prime factors of 28 are 2,2,7.
If we multiply the prime factors we get 28.
Therefore , the prime factorisation of 28 is $2 \times 2 \times 7$.
Method 2: Prime factorisation by factor tree method
In this method we draw the factor tree with least prime factor. The normal prime factors are 2,3,5,7,11,1,17,19 and so on .
Let us draw the factor tree

Therefore , the prime factorisation of 28 is $2 \times 2 \times 7$.

Note:
The prime factors of a number are the prime numbers that when multiplied it gives the original number. The second method factor tree method is used to determine the factors of natural numbers which are greater than one.