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On dividing the numbers 7654, 8506 and 9997 by a certain largest number, in each case the remainder is the same. Find the number and the remainder.
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- 213 and 199
- 223 and 189
- 233 and 179
- None of these
Correct Option: A
Let the remainder be t. Then (7654 – t), (8506 – t) and (9997 – t) are exactly divisible by that number.
Hence the required number
= HCF of (7654 – t),(8506 – t) and (9997 – t)
= HCF of (8506 – t) – (7654 – t), (9997 – t) – (8506 – t) and (9997 – t) – (7654 – t) = HCF of 852, 1491 and 2343
Now, HCF of 213 and 2343
Hence required number = 213
Required remainder = 7654 ÷ 213
Hence required remainder = 199
