Question

What is the greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively?

• A. 95
• B. 71
• C. 83
• D. 73

Answer 1

Answer:

D. 73

If the integer leaves remainder 43, on dividing 554, then it divides 511 exactly If the integer leaves remainder 57, on dividing 714, then it divides 657 exactly If the integer leaves remainder 67, on dividing 213, then it divides 146 exactly prime factorizing 511, 657 and 146 511 = 7 × 73 657 = 3 × 3 × 73 146 = 2 × 73 HCF of 511, 657 and 146 = 73