Tips on Factoring Help

Factoring Tips - Rules of Divisibility

Factoring is a skill that is developed with practice. The only surefire way to factor numbers into their prime factors is by trial and error. There are some number facts that will make your job easier. Some of these facts should be familiar.

• If a number is even, the number is divisible by 2.
• If a number ends in 0 or 5, the number is divisible by 5.
• If a number ends in 0, the number is divisible by 10.
• If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
• If a number ends in 5 or 0 and the sum of its digits is divisible by 3, then the number is divisible by 15.
• If a number is even and the sum of its digits is divisible by 3, then the number is divisible by 6.
• If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.
• If the sum of the digits of a number is divisible by 9 and the number is even, then the number is divisible by 18.

Examples

Factoring Tips - Identifying the Prime Factors

To factor a number into its prime factors (those which have no divisors other than themselves and 1), start with a list of prime numbers (a short list can be found on the last page of this appendix). Begin with the smallest prime number and keep dividing the prime numbers into the number to be factored. It might be that a prime number divides a number more than once. Stop dividing when the square of the prime number is larger than the number. The previous list of number facts can help you ignore 2 when the number is not even; 5 when does not end in 5; and 3 when the sum of its digits is not divisible by 3.

Examples

Find practice problems and solutions at Tips on Factoring Practice Problems - Set 1.

Factoring Tips - Prime Factorization

To factor a number into its prime factors, keep dividing the number by the prime numbers in the list. A prime number might divide a number more than once. For instance,

12 = 2 × 2 × 3.