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## Finding All Prime Factors Of A Number

We arrived at our answers for prime factors by using the factor tree. However we could have also used upside-down division to get the factorization primes. There are more that one method to factorize a number.

## List of divisibility rules for finding prime factors faster

Rule 1: If the last digit of a number is 0, 2, 4, 6 or 8 then it is an even number. All even numbers are divisible by 2 and 2 is a prime factor.

Rule 2: If the sum of digits of a number is divisible by 3 then the number is also divisible by 3 and 3 is a prime factor(example: the digits of 12 are 1 and 2 so 1+2=3 and 3 is divisible by 3, meaning that 12 is divisible by 3). The same logic works also for number 9.

Rule 3: If the last two digits of a number are 00 then this number is divisible by 4(example: we know that 124=100-24 and 100 has two zeros in the end making it divisible with 4. We also know that 4 is divisible with 24). In order to use this rule to it's fullest it is best to know multiples of 4.

Rule 4: If the last digit of a number is 0 or 5 then 5 it is divisible by 5 and 5 is a prime factor.

Rule 5: All numbers that are divisible by both 2 and 3 are also divisible by 6.

## What Are Prime Factors Of A Number?

All numbers that are only divisible by one and itself are called prime factors in mathematics. A prime factor is a number that has only two factors(one and itself).