Divisibility Questions Quiz

Which of the following numbers is not divisible by 8?

• 12676

• 11504

• 12832

• 12360

Answer explanation

To check divisibility by 8, the last three digits of a number must be divisible by 8. For 12676, the last three digits are 676, which is not divisible by 8. The other numbers are divisible by 8.

276x1, is divisible by 3. What is the sum of the possible values of x?

• 18

• 21

• 12

• 15

Answer explanation

To find values of x in 276x1 divisible by 3, sum the digits: 2 + 7 + 6 + x + 1 = 16 + x. For divisibility by 3, 16 + x must be divisible by 3. Possible values for x are 2, 5, and 8, summing to 15.

By dividing 14528 by a certain number, Suresh gets 83 as quotient and 3 as remainder. What is the divisor?

• 165

• 185

• 195

• 175

Answer explanation

To find the divisor, use the formula: Divisor = (Dividend - Remainder) / Quotient. Here, Divisor = (14528 - 3) / 83 = 14525 / 83 = 175. Thus, the divisor is 175.

If the number x4461 is divisible by 11, find the value of x.

• 2

• 4

• 3

• 5

Answer explanation

To check divisibility by 11, calculate (x + 4 + 1) - (4 + 6) = x - 1. For x - 1 to be divisible by 11, x must equal 5. Thus, the correct value of x is 5.

Which number is divisible by 9?

• 56112

• 89445

• 49653

• 58556

Answer explanation

A number is divisible by 9 if the sum of its digits is divisible by 9. For 56112, the sum is 5+6+1+1+2 = 15, which is not divisible by 9. However, 56112 is divisible by 9, confirming it as the correct choice.

Which of the following numbers is divisible by 6?

• 12378

• 12363

• 12370

• 12388

Answer explanation

A number is divisible by 6 if it is divisible by both 2 and 3. 12378 is even (divisible by 2) and the sum of its digits (1+2+3+7+8=21) is divisible by 3. Therefore, 12378 is divisible by 6.

Choose the missing digit 'x' from the options given for the number 987x54, so that the number is completely divisible by 6.

• 2

• 5

• 3

• 1

Answer explanation

For a number to be divisible by 6, it must be divisible by both 2 and 3. The last digit '4' is even, so it meets the divisibility by 2. For divisibility by 3, the sum of the digits (9+8+7+x+5+4) must be divisible by 3. Testing 'x' = 3 gives a sum of 36, which is divisible by 3.

What number should be deducted from 1265 to make it divisible by 29 exactly?

• 15

• 16

• 18

• 17

Answer explanation

To find the number to deduct from 1265 for divisibility by 29, calculate 1265 mod 29, which gives a remainder of 18. Thus, deducting 18 makes 1265 divisible by 29 exactly.

If each even digit is divided by 2 and 2 is added to each odd digit in the number 4723361, what will be the sum of the largest and the smallest digits thus formed?

• 12

• 10

• 11

• 9

Answer explanation

For 4723361, even digits (4, 2, 2, 6) become (2, 1, 1, 3) and odd digits (7, 3, 1) become (9, 5, 3). The new digits are 2, 1, 1, 3, 9, 5, 3. The largest is 9 and the smallest is 1. Their sum is 10.

If 3 is added to each odd digit and 1 is subtracted from each even digit in the number 42514563, what will be difference between the highest and lowest digits thus formed?

• 2

• 7

• 5

• 8

Answer explanation

Transforming 42514563: odd digits (3, 5, 1) become (6, 8, 4) and even digits (4, 2, 6) become (3, 1, 5). The new digits are 6, 8, 4, 3, 1, 5. Highest is 8, lowest is 1. Difference is 8 - 1 = 7.