On being divided by a three-digit number, the numbers 98558 and 93675 leave the same remainder. Find the number and the remainder?a)223 & 115b)257 & 127c)233 & 117d)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

To find the number and remainder when divided by a three-digit number, we subtract the two given numbers and find the greatest common divisor (GCD) of the result and the three-digit number.

98558 - 93675 = 4875

The GCD of 4875 and a three-digit number will be the remainder when divided by that three-digit number.

To find the GCD, we can use the Euclidean algorithm.

4875 ÷ 223 = 21 remainder 12
223 ÷ 12 = 18 remainder 7
12 ÷ 7 = 1 remainder 5
7 ÷ 5 = 1 remainder 2
5 ÷ 2 = 2 remainder 1
2 ÷ 1 = 2 remainder 0

The GCD of 4875 and 223 is 1.

Therefore, the three-digit number is 223 and the remainder is 1.

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