Prime Factorization of Numbers
Prime factors of a given number are the prime numbers which multiply together to make the given number.
Consider the number 6, we can write the prime factorization of 6 as shown below:
6 = 2 x 3
Prime factorization for 30 is as shown below:
30 = 2 x 3 x 5
Keep in mind that always try to find 2s, 3s and 5s in the prime factorization of a given number. Following are the divisibility tests for these three basic prime number:
1. Divisibility test for 2: All the even numbers are divisible by 2. In other words if the ones digit of a number is 0, 2, 4, 6 or 8 then this number is divisible by 2.
For example; 48 is an even number hence divisible by 2. On the other hand 127 is an odd number hence not divisible by 2.
2. Divisibility test for 3: Add all the digits of the given number if the sum is divisible by 3 then the given number is divisible by 3.
For example; consider 15. To test for the divisibility by 3 let's add both the digits (1 and 5) = 1+5 = 6. Now 6 is divisible by 3 hence 15 is divisible by 3.
2. Divisibility test for 5: If the ones digit is either 0 or 5 then the given number will be divisible by 5.
For example; consider 80. Ones digit is 0 hence 80 is divisible by 5.
How to find prime factorization of a number:
There are following two ways to find the prime factorization of a given number:
