# Divisibility Problems

## Divisibility Problems

Problems on divisibility rules will help us to learn how to use the rules to test of divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

### Divisibility by 2

**Rule: **The last digit which is either even or 0, is divisible by 2. **Example** 34, 2532, 1290

### Divisibility by 3

**Rule: **If the sum of the digits of a number is divisible by 3, then the number is also divisible by 3 **Example** 2451, so required sum 2+4+5+1=12 divisible by 3 so the number 2451 is also divisible by 3

### Divisibility by 4

**Rule 1: ** If the last two digits of a number is divisible by 4, the number is also divisible by 4

**Rule 2: **The number having two or more zeros at the end is also divisible by 4

**Example **728524 since the last two digits are divisible by 4 so the number is also divisible by 4. **Example **15600 last two digits are 00 so the number is also divisible by 4.

### Divisibility by 5

**Rule: **If a number ends with 5, 0 then the number will be divisible by 5 **Example **1765, 12330

### Divisibility by 6

For this both two rule should be full filled

**Rule 1: **The number should end with an even digit or 0.

**Rule 2: **The sum of the digits should divisible by 3.

**Example **174 is divisible by 6 as the number ends with even digit 4 and sum of the digits 12 is divisible by 3

**Example **8520 is divisible by 6, as it ends with 0 and sum of the number 15 is divisible by 3

### Divisibility by 7

There is no any stritct rule for it

**Example** 896 Solution: 896 89-6*2=77 as 77 is divisible to 7 so this number 896 is also divisible to 7

**Example** 4753 Solution: 475-3*2= 469 46-9*2=28 as 28 is divisible by 7 so the number 4753 is divisible to 7

### Divisibility by 8

**Rule 1: ** If the last three digits of the number is divisible by 8 , the number is also divisible by 8

**Rule 2: ** If the last three digits of the number is three zeros 000 then the number is also divisible to 8

**Example** 14873258376256 find out divisibilty by 8. Solution: 14873258376256 is divisible to 8 , so the whole number is divisible to 8

### Divisibility by 9

**Rule:** If the sum of all the digits of a number is divisible by 9, hence the number is also divisible by 9. **Example** 8758323 Solution: Sum of the number is 8+7+5+8+3+2+3=36 which is divisile by 9, so the number is divisible by 9

### Divisibility by 11

**Rule: **If the sum of the digits at odd places and even places are equal or differ by an amount of 11, then the number will be divisible by 11

**Example **589743671 Check the divisibilty by 11 Solution: Sum of the digits at odd places 5+9+4+6+1=25 Sum of the digits at even places 8+7+3+7=25 So the number is divisible by 11

**Example **9754239 check the divisibility by 11 Solution: Sum of the numbers at odd places 9+5+2+9=25 Sum of the numbers at even places 7+4+3=14, the difference 25-14=11, so the number will be divisible by 11

### Divisibility by 12

**Rule: **Any number which is divisble by both 4 and 3, is also divisible by 12

### Divisibility by 14

**Rule: **for divisibility with 14, the number should be even and should be divisible by 7

### Divisibility by 15

**Rule: **Any number which is divisible by both 3 and 5 is also divisible by 15

### Divisibility by 16

**Rule: **any number whose last four digits number is divisile by 16 is also divisible by 16