# Problems on Divisibility Rules

Here are few problems on the divisibility rules of 2, 3, 4, 5, 6, 7, 8, 9, and 10 which will help the learners in revising their concepts on the divisibility rules.

1. Check whether 3456 is divisible by 2?

Solution:

The last digit is an even number (i.e. 6) hence 3456 is divisible by 2

2. Check whether 8577 is divisible by both 3 and 9?

Solution:

Um of the digits = 8 + 5 + 7 + 7 = 27

27 is divisible by 3 hence, the number is also divisible by 3.

Now, 27 is also divisible by 9, soothe number is divisible by 9

Hence, 8577 is divisible by both 3 and 9

3. Check whether 40800 is divisible by:

i) 5                   ii) 10                iii) 25

Solution:

i) We know that if the last digit is 0 or 5 then the number is divisible by 5

Hence 40800 is divisible by 5

ii) As the last digit is 0 hence the number is divisible by 10

iii) According to the divisibility rule if a number has last two digits 0 or the number formed by last two digits is a multiple of 25 then the number is divisible by 25. Here in 40800 the last two digits is 0 hence the number in divisible by 25.

iii) If a number has last two digits 00, 25, 50 or 75 then the number is divisible by 25. Here, in 40800 the number ends with 00 hence, it is divisible by 25.

4. Is 2584 is divisible by both 2 and 4?

Solution:

The last digit is an even number hence the number is divisible by 2.

The number formed by the last two digits of 2584 is 84

Now, 84 is divisible by 4 and it gives 21

Hence, 2584 is divisible by both 2 and 4

5. Check which of the following numbers are divisible by 5 or 10 or both of them?

(i) 545

(ii) 8795

(iii) 3400

(iv) 6490

(v) 45220

Solution:

(i) 545

The last digit is 5 hence it is divisible by 5 but not divisible by 10.

(ii) 8795

The last digit is 5 hence it is divisible by 5 but not divisible by 10.

(iii) 3400

The last digit is 0 hence divisible by both 5 and 10.

(iv) 6490

The last digit is 0 hence divisible by both 5 and 10

(v) 45220

45220 has the last digit 0 hence, divisible by both 5 and 10

6. Is 9486 is divisible by 9? State whether the number is also divisible by 18 also?

Solution:

Sum of the digits = 9 + 4 + 8 + 6 = 27

As, 27 is divisible by 9 hence, 9486 is also divisible by 9

Moreover, the last digit is a even number that is 6 hence it is divisible by 2 as well.

Now, if a number is divisible by both 9 and 2 then the number is also divisible by 18

Yes, 9486 is divisible by 18

7. Check whether 1302 is divisible by 6?

Solution:

Sum of the digits = 1 + 3 + 0 + 2 = 6

As, 6 is divisible by 3, hence 1302 is also divisible by 3

Moreover, the last digit of 1302 is an even number (i.e. 2)

Hence, it is divisible by 2

As, 1302 is divisible by both 3 and 2 hence, it is also divisible by 6

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