The greatest number that divides 415, 688 and 825 leaving 7, 8 and 9 as remainders, respectively, is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 136.
Numbers which are completely divisible = (415 - 7) = 408
= 688 - 8 = 680 and
= 825 - 9 = 816
By prime factorization, we get
⇒ 408 = 23 × 3 × 17
⇒ 680 = 23 × 5 × 17
⇒ 815 = 24 × 3 × 17
Required HCF = 23 × 17 = 8 × 17
= 136