Page 75 - Touchpad Mathematics_Ver1.0_C5

E:\Working\Orange_Education\TouchPad_Maths-5\Open file\Maths_5_Chapter-03
\ 19-Nov-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

diviSiBiliTY TeSTS

When we divide one number by another and get 0 as the remainder, the first number
is said to be divisible by the second number.

Here, we divide both 85 and 88 by 5. 1 7 1 7

On dividing 85 by 5, we get a remainder of 0. So, 85 is 5 8 5 5 8 8
divisible by 5. – 5 – 5
On dividing 88 by 5, we get a remainder of 3 instead of 0. 3 5 3 8

So, 88 is not divisible by 5. – 3 5 – 3 5
Just by following some rules, we can say whether a number 0 3

is exactly divisible by another number or not.
This method of determining whether a given number is exactly divisible by another
number or not is called the test of divisibility.

Test of divisibility by 2: All even numbers are divisible by 2.

For example, 10, 12, 14, 16, 18, 24, 102, 1004, ...... are all divisible by 2.

A number is divisible by 2 if it has the last digit (or digit in the ones place) 0, 2, 4, 6 or 8.

Test of divisibility by 3: Study the following table.

Numbers Sum of the digits is the sum divisible is the number
by 3? divisible by 3?

15 1 + 5 = 6 Yes Yes

144 1 + 4 + 4 = 9 Yes Yes

5443 5 + 4 + 4 + 3 = 16 No No

8004 8 + 0 + 0 + 4 = 12 Yes Yes

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

Test of divisibility by 5: Look at the following:

15 ÷ 5 = 3, 20 ÷ 5 = 4, 35 ÷ 5 = 7, 100 ÷ 5 = 20

A number is divisible by 5, if it has 0 or 5 in its ones place.

Test of divisibility by 10: Observe the following:

10 ÷ 10 = 1, 20 ÷ 10 = 2, 400 ÷ 10 = 40, 550 ÷ 10 = 55

A number is divisible by 10, if its last digit (ones digit) is 0.

73
Multiples and Factors