When factoring algebraic expressions so you can solve equations, you need to understand the rules of divisibility to be able to pull out the greatest factor. Also, common factors are needed when reducing algebraic fractions. The rules of divisibility help you to find the common factors and change the algebraic expressions so that they’re put in a more workable form.

**Divisibility by 2:**A number is divisible by 2 if the last digit in the number is 0, 2, 4, 6, or 8.**Divisibility by 3:**A number is divisible by 3 if the sum of the digits in the number is divisible by 3.**Divisibility by 4:**A number is divisible by 4 if the last two digits in the number form a number divisible by 4.**Divisibility by 5:**A number is divisible by 5 if the last digit is 0 or 5.**Divisibility by 6:**A number is divisible by 6 if it is divisible by both 2 and 3.**Divisibility by 8:**A number is divisible by 8 if the last three digits form a number divisible by 8.**Divisibility by 9:**A number is divisible by 9 if the sum of the digits of the number is divisible by 9.**Divisibility by 10:**A number is divisible by 10 if it ends in 0.**Divisibility by 11:**A number is divisible by 11 if the sums of the alternate digits are different by 0, 11, 22, or 33, or any two-digit multiple of 11. In other words, say you have a six-digit number: Add up the first, third, and fifth digits — the odd ones. Then add the digits in the even places — second, fourth, and sixth. Then subtract the smaller of those totals from the larger total, and if the answer is a multiple of 11, the original number is divisible by 11.**Divisibility by 12:**A number is divisible by 12 if the last two digits form a number divisible by 4 and if the sum of the digits is divisible by 3.