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Question 85

If the positive integer 1541, 2444, 2659 leave the same remainder when divided by a positive integer m, then the largest value of m is

Solution

As per the given data in the question,

When these number are divided by m, then 1541, 2444, 2659 it is leaving the same remainder.

Now, (2444-1541=903) and (2659-2444=215) and (2659-1541=1118)

HCF, of these numbers, $$903=43\times 7\times 3$$

$$215=5\times 43$$

And $$1118=43\times 13\times 2$$

Hence, from the above it is clear that 43 is the largest value of m.

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