Question

Find the largest number by which when 270, 675 and 1215 are divided, leave equal remainder in each case.

A. 45

B. 135

C. 270

D. 75

1. D
2. B
3. C
4. A

Answer 1

Correct Answer - Option 2 : B

Given:

Numbers are 270, 675, 1215

Calculation:

Let us assume that the remainder left is m

So, numbers that are completely divisible are

⇒ 270 – m, 675 – m, 1215 – m

Now subtract the pair

⇒ 675 – m – 270 + m = 405      ----1

⇒ 1215 – m – 675 + m = 540      ----2

Now find the HCF of 405 and 540

⇒ 405 = 135 × 3

⇒ 540 = 135 × 4

HCF of 405 and 540 = 135

∴ The largest number by which 270, 675 and 1215 are divided, leave the equal remainder in each case is 135