Question : Find the greatest number which when divided 261, 853, and 1221, leaves a remainder of 5 in each case.
Option 1: 19
Option 2: 18
Option 3: 17
Option 4: 16
Correct Answer: 16
Solution :
The greatest number that divides 261, 853, and 1221, leaving a remainder of 5 in each case, is the greatest common divisor (GCD) of (261 – 5), (853 – 5), and (1221 – 5).
So, we need to find the GCD of 256, 848, and 1216.
The GCD of these numbers is 16.
So, 16 is the greatest number which Divides the numbers 261, 853, and 1221, leaving a remainder of 5 in each case.
Hence, the correct answer is 16.
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