Divisibility Rules of 2, 4 and 8
Concept: The Divisibility Rules help us to determine if a number will divide into another number without actually having to divide. Rules can be made for any of the number but here we will learn the most common ones
Prerequisite: One should know basic tables.
1. The Rule for 2
Any whole number that ends in 0, 2, 4, 6, & 8 will be divisible by 2 or last digit divisible by 2. Then the complete number is said to be divisible by 2.
| Number | Divisible? | Why? |
| 786 | Yes | As we can see number ends with ‘6’ so complete number is divisible by 2 |
| 28 | Yes | As we can see number ends with ‘8’ so complete number is divisible by 2 |
| 197 | No | As we can see number ends with ‘7’ so number is not divisible by 2 |
2. The Rule for 4
If the last two digits are multiple of 4 or divisible by 4 or last 2 digits are ’00’, then the complete number is said to be divisible by 4.
Suppose if number is 1524 then look at last 2 digits ‘24’ which is a multiple of 4, so complete 1524 is divisible by 4.
| Number | Divisible? | Why? |
| 936 | Yes | Here last 2 digits are ‘36’ which is a multiple of 4 |
| 1012 | Yes | Here last 2 digits are ‘12’ which is a multiple of 4 |
| 1097 | No | Here last 2 digits are ‘97’ which is not a multiple of 4 |
3. The Rule for 8:
If the last three digits are multiple or divisible by 8 or if the last three digits are ‘000’
Suppose if number is 12520 then look at last 2 digits ‘520’ which is a divisible by 8.
| Number | Divisible? | Why? |
| 21832 | Yes | Here last 3 digits are ‘832’ which is a multiple of 8 |
| 329248 | Yes | Here last 3 digits are ‘248’ which is a multiple of 8 |
| 19113 | No | Here last 3 digits are ‘113’ which is a not multiple of 8 |