# Divisibility

A number,** b**, is** divisible by** another** number, a,** if the division is exact.

## Rules of Divisibility

### Divisible by 2

A number is divisible by **2**, if* its last digit is a zero or an even number. *

24, 238, 1,024.

### Divisible by 3

A number is divisible by **3**, if *the sum of its digits is a multiple of 3.*

564

5 + 6 + 4 = 15, is multiple 3

2,040

2 + 0 + 4 + 0 = 6, is multiple 3

### Divisible by 5

A number is divisible by **5**, if it ends in zero or five.

45, 515, 7,525.

### Divisible by 7

A number is divisible by **7***, when the difference between the number without the figure of the units and the double the number of the units is 0 or a multiple of 7*.

343

34 − 2 · 3 = 28, is multiple of 7.

105

10 − 5 · 2 = 0

2261

226 - 1 · 2 = 224.

Repeat the process with 224.

22 − 4 · 2 = 14, is multiple of 7.

### Divisible of 11

A number is divisible by **11**, if* the difference between the sum of the figures who occupy the even numbers and the odd numbers is 0 or a multiple of 11*.

121

(1 + 1) − 2 = 0

4,224

(4 + 2) − (2+4) = 0

## Other rules

### Divisible by 4

A number is divisible by **4**, if the last two digits are zeros or a multiple of 4.

36, 400, 1,028.

### Divisible by 6

A number is divisible by **6**, if it is divisible by 2 and 3.

72, 324, 4,200.

### Divisible by 8

A number is divisible by **8**, if* its last three figures are zeros or a multiple of 8. *

4000, 1048, 1512.

### Divisible by 9

A number is divisible by 9, if* the sum of its digits gives a multiple of 9.*

81

8 + 1 = 9

3,663

3 + 6 + 6 + 3 = 18, is multiple of 9

### Divisible by 10

A number is divisible by **10**,* if the last figure in the unit is 0.*

130, 1,440, 10,230

### Divisible by 25

A number is divisible by **25**, if their last two digits are zeros or a multiple of 25.

500, 1,025, 1,875.

### Divisible by 125

A number is divisible by **125**, if its last three figures are zeros or a multiple of 125.

1,000, 1,125, 4,250.

#### Factoring

Factoring a number into prime factors is to express the number as a product of prime numbers.