## Test for Divisibility of Numbers by 10, 5, and 2

Divisibility of numbers by a number can be checked by observing patterns of numbers. Using this technique, divisibility of numbers can be checked without performing actual division.

### (a) Divisibility by 10

Divisibility of a number by 10 can be checked very easily.

If a number ends with zero, then the number will be divisible by 10. In other words, if a number has **zero (0)** at its ones place, then the number is divisible by 10.

**Example**

(i) 20: Since, 20 has zero (0) at its ones place, hence 20 is divisible by 10.

If we divide 20 by 10 we get 2 as quotient.

(ii) 30: Since, 30 has zero (0) at its ones place, hence 20 is divisible by 10.

We get 3 when divide 30 by 10.

(iii) 100: Since, 100 has zero (0) at its ones place, hence 100 is divisible by 10.

We get 10 as quotient when 100 is divided by 10.

(iv) 5550: Since, 5550 has zero (0) at its ones place, hence 5550 is divisible by 10.

5550 ÷ 10 = 555

### (b) Divisibility by 5

If a number ends with either fiver (5) or zero (0), then the number is divisible by 5.

In other words, if a number has five (5) or zero (0) at its ones place, then the number will be divisible by 5.

**Example (1): Numbers have 5 at ones place are divisible by 5**

(i) 15: Since 15 has 5 at its ones place, hence 15 is divisible by 5.

15 ÷ 5 = 3

(ii) 25: Since 25 has 5 at its ones place, hence 25 is divisible by 5.

25 ÷ 5 = 5

(iii) Since 35 has 5 at its ones place, hence 35 is divisible by 5.

35 ÷ 5 = 7

(iv) Since 105 has 5 at its ones place, hence 105 is divisible by 5.

105 ÷ 5 = 21

**Example (2): Numbers have 0 at ones place are divisible by 5**

(i) 10: Since 10 has zero (0) at its ones place, hence 10 is divisible by 5.

10 ÷ 5 = 2

(ii) 20: Since 20 has zero (0) at its ones place, hence 20 is divisible by 5.

20 ÷ 5 = 4

(iii) Since 30 has zero (0) at its ones place, hence 30 is divisible by 5.

30 ÷ 5 = 6

(iv) Since 100 has zero (0) at its ones place, hence 100 is divisible by 5.

100 ÷ 5 = 20

Thus, numbers having zero (0) at their ones place, are divisible by five (5) and ten (10) both.

### (c) Divisibility by 2

Numbers having 2, 4, 6, 8, or zero (0) at their ones place are divisible by 2.

This means numbers having even numbers or zero at their ones place are divisible by 2.

**Example (i): Numbers having 2 at their ones place are divisible by 2**

(i) 12: Since 12 has 2, an even number at its ones place hence, 12 is divisible by 2.

12 ÷ 2 = 6

(ii) 52: Since 52 has 2, an even number at its ones place hence, 52 is divisible by 2.

52 ÷ 2 = 26

**Example (ii): Numbers having 4 at their ones place are divisible by 2**

(i) 14: Since 14 has 2, an even number at its ones place hence, 14 is divisible by 2.

14 ÷ 2 = 7

(ii) 54: Since 54 has 2, an even number at its ones place hence, 54 is divisible by 2.

54 ÷ 2 = 27

**Example (iii): Numbers having 6 at their ones place are divisible by 2**

(i) 16: Since 16 has 2, an even number at its ones place hence, 16 is divisible by 2.

16 ÷ 2 = 8

(ii) 56: Since 56 has 2, an even number at its ones place hence, 56 is divisible by 2.

56 ÷ 2 = 28

(iii) 106: Since 106 has 2, an even number at its ones place hence, 106 is divisible by 2.

106 ÷ 2 = 53

**Example (iv): Numbers having 8 at their ones place are divisible by 2**

(i) 18: Since 18 has 2, an even number at its ones place hence, 18 is divisible by 2.

18 ÷ 2 = 9

(ii) 58: Since 58 has 2, an even number at its ones place hence, 58 is divisible by 2.

58 ÷ 2 = 29

(iii) 108: Since 108 has 2, an even number at its ones place hence, 108 is divisible by 2.

108 ÷ 2 = 54

**Example (v): Numbers having 8 at their ones place are divisible by 2**

(i) 18: Since 18 has 2, an even number at its ones place hence, 18 is divisible by 2.

18 ÷ 2 = 9

(ii) 58: Since 58 has 2, an even number at its ones place hence, 58 is divisible by 2.

58 ÷ 2 = 29

(iii) 108: Since 108 has 2, an even number at its ones place hence, 108 is divisible by 2.

108 ÷ 2 = 54

**Example (vi): Numbers having zero (0) at their ones place are divisible by 2**

(i) 10: Since 10 has zero (0) at its ones place hence, 10 is divisible by 2.

10 ÷ 2 = 5

(ii) 50: Since 50 has zero (0) at its ones place hence, 50 is divisible by 2.

50 ÷ 2 = 25

(iii) 100: Since 100 has zero (0) at its ones place hence, 100 is divisible by 2.

100 ÷ 2 = 50

(iv) 550: Since 550 has zero (0) at its ones place hence, 550 is divisible by 2.

550 ÷ 2 = 275