Which is the largest number that will divide 1992 and 233 leaving remainders 12 and 13 respectively ........

Quantitative Aptitude (MTS) Number System

Which is the largest number that will divide 1992 and 233 leaving remainders 12 and 13, respectively?

This questions was previously asked in

SSC MTS 2nd Nov 2021 Shift-2

242

220

246

186

To solve this problem, we need to find the largest number \( d \) such that:

- \( 1992 - 12 = 1980 \) is divisible by \( d \).

- \( 233 - 13 = 220 \) is divisible by \( d \).

Thus, \( d \) should be the greatest common divisor (GCD) of 1980 and 220.

- List the factors:

- Factors of 1980: \( 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980 \)

- Factors of 220: \( 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220 \)

- The greatest common factor from these lists is 220.

- Therefore, the largest number that divides both 1980 and 220 is 220.

- Correct Answer: Option 2: 220

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