How Do You Know if a Number is Divisible by 2, 3, 5, 6, or 10?

In order to determine if 436 is divisible by 2, we look at known multiples of 2
In order to determine if 867 is divisible by 3, we add the digits and if their sum is divisible by 3, then the original number is divisible by 3
In order to determine if 675 is divisible by 5, we look at known multiples of 5
In order to determine if 732 is divisible by 6, it must be divisible by both 2 and 3, the prime factors of 6
In order to determine if 580 is divisible by 10, look at known multiples of 10 and you'll see they all end in 0

1. First, think about numbers we know are multiples of 2
2. 2, 4, 6, 8, ... are all multiples of 2
3. These are all EVEN numbers!
4. So if we have an even number, it will be divisible by 2
5. Since 436 is an even number, it's divisible by 2
1. Here's a handy little trick that will help us:
2. If you add up all the digits in the number, and the number you get is divisible by 3, then that number is also divisible by 3!
1. First, think about numbers we know are multiples of 5
2. 5, 10, 15, 20, 25, 30, ... are all multiples of 5
3. There's a pattern here:
4. All these multiples of 5 end in 0 or 5!
5. This is true for all multiples of 5
6. Since 675 ends in 5, it's divisible by 5
1. This one is a bit trickier!
2. But if we factor 6 into its prime factors, we find it equals 2•3
3. So every multiple of 6 is also going to be a multiple of 2 and 3
4. Therefore, if a number is divisible by both 2 AND 3, then it's also divisible by 6!
5. Since 732 is even, it's divisible by 2, and since 7+3+2 is 12, which is divisible by 3, 732 is divisible by 6
1. First, think about numbers we know are multiples of 10
2. 10, 20, 30, 40, ... are all multiples of 10
3. All of these numbers end in 0!
4. This is true for all multiples of 10, so 580 is divisible by 10 since it ends in 0

Definition: Divisibility Rules for 2, 3, 5, 6, and 10