Best Answer

The smallest number that satisfies the problem is 1718366.

There is no greatest number; whatever value you specify as the greatest I can add 967 × 2053 = 1985251 and get an even greater number that solves the problem. This addition is divisible by both 2053 and 967, so when dividing by 2053 or 967 the (respective) remainder does not change.

Q: What is the greatest number which when divided by 2053 and 967 leaves a remainder of 5 and 7 respectively?

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It is an integer which, when divided by 2, leaves a remainder of 1.

2

209

11

18

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It is an integer which, when divided by 2, leaves a remainder of 1.

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No answer is possible as any number divided by 9 must either be exactly divisible by 9 or leave a remainder less than 9.

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