Divisibility Rules in Reference with Factors

Q.

Which of the following number is divisible by 5 and 10 both?

1. 45

2. 450

3. 412

4. 405

Q.

Given that 312 is divisible by 26. It will also be divisible by ________.

1. 13

2. 7

3. 9

4. 11

Q. If the square of a two digit number is decreased by the square of the number formed by reversing the digits , then the result is not always divisible by :
(A) 9
(B) the products of the digits
(C) the sum of the digits
(D) the difference of the digits

Q. If the sum of digits of a number is divisible by three, and the units digit is an even number, then the number is always divisible by

1. 3 only
2. 6 only
3. 2 only
4. Both 3 and 6

Q. If the sum of digits of a number is divisible by three, and the units digit is an even number, then the number is always divisible by

1. 3 only
2. 6 only
3. 2 only
4. Both 3 and 6

Q. If a number is divisible by 12, it is also divisible by ___ .

1. 6
2. 2
3. 3
4. 4

Q. If 35 and 20 are divisible by 5, then their difference is divisible by

1. 5
2. 2
3. 4

Q. Which of the statement(s) is/are false?

1. If a number ‘a' is divisible by another number 'b', then it is divisible by each of the factors of that number 'b'.
2. If 'a’ and ‘b’ have no common factors (other than unity), the number divisible by ‘a’ and ‘b’ is also divisible by a × b.
3. If two given numbers are divisible by a number, then their sum is also divisible by that number.
   
4. None of these

Q. $2^3$ + $2^4$ + $2^5$ + ....... + $2^n$, where n > 0,
is always divisible by .

1. 2
2. 10
3. 5
4. 9

Q. If 144 is divisible by 12, it is also divisible by

1. 6
2. 9
3. 11

Q. (1567 x 1568 x 1569) is divisible by which of the following number(s)?

1. 3
2. 6
3. 2
4. 5

Q.

Prove that if I add a number to itself, the resulting number is divisible by 2.
[2 MARKS]

Q.

Which of the following numbers is divisible by 99?

1. 913462

2. 114345

3. 135792

4. 3572406

Q. Among 2, 3 and 9, the number 48 is divisible by ___.

1. 3 only
2. 2 and 3 only
3. 2, 3 and 9
4. 2 only

Q. If a number is divisible by 90, it is also divisible by:

1. 45
2. 7
3. 11
4. 12

Q. If 148 and 224 are divisible by 4, then their sum is divisible by .

1. 4
2. 7
3. 9