# How can you tell whether a number is divisible by another number (leaving no remainder) without actually doing the division?

**A Number is Divisibility by:**

**2 :**If the last digit is even, the number is divisible by 2.

**3 :**If the sum of the digits is divisible by 3, the number is also.

**4 :**If the last two digits form a number divisible by 4, the number is also.

**5 :**If the last digit is a 5 or a 0, the number is divisible by 5.

**6 :**If the number is divisible by both 3 and 2, it is also divisible by 6.

**7 :**Take the last digit, double it, and subtract it from the rest of the number; if the answer is divisible by 7 (including 0), then the number is also.

**8 :**If the last three digits form a number divisible by 8, then so is the whole number.

**9 :**If the sum of the digits is divisible by 9, the number is also.

**10 :**If the number ends in 0, it is divisible by 10.

**11 :**Alternately add and subtract the digits from left to right. If the result (including 0) is divisible by 11, the number is also. Example: to see whether 365167484 is divisible by 11, start by subtracting: 3-6+5-1+6-7+4-8+4 = 0; therefore 365167484 is divisible by 11.

**12 :**If the number is divisible by both 3 and 4, it is also divisible by 12.

**13 :**Delete the last digit from the number, then subtract 9 times the deleted digit from the remaining number. If what is left is divisible by 13, then so is the original number.