Multiple choice

Find the greatest number which on dividing 63, 135 and 243 leaves the same remainder in each case.

  1. 6

  2. 12

  3. 36

  4. 48
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C Correct answer
Explanation

Find the differences: 135-63 = 72, 243-135 = 108, 243-63 = 180. The HCF of 72, 108, and 180 is 36.

AI explanation

To find the greatest number that leaves the same remainder when dividing 63, 135 and 243, apply the greatest common divisor (GCD) method to the differences between the numbers. Calculate the differences 135 minus 63 equals 72, and 243 minus 135 equals 108. The required number is the HCF of 72 and 108; since the highest common factor is 36, the required number is 36.

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