Find the greatest number that will divide 49, 147 and 322 to leave the same remainder in each case

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 1)

Answer 1

Given:

The greatest number that will divide 49, 147 and 322 to leave the same remainder in each case

Concept used:

We must now identify differences between the provided numbers.

When two numbers are divided by another number and have the same remaining, their difference must produce a remainder of zero.

Calculations:

According to the question,

The differences will be,

⇒ 147 - 49 = 98

⇒ 322 - 147 = 175

⇒ 322 - 49 = 273

The set of numbers {98,175,273}

Now HCF of {98,175,273}

⇒ 98 = 7 × 7 × 2

⇒ 175 = 5 × 5 × 7

⇒ 273 = 13 × 7 × 3

The HCF of {98,175,273} is 7

∴ The same remainder in each case is 7.

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