What is the greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively?
a) 70
b) 73
c) 77
d) 75
Sol:
Given:
Integers 554, 714 and 213
Concept Used: HCF = Highest Common Factor
Calculation:
⇒ According to the question,
⇒ 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
⇒ On prime factorizing 511, 657 and 146, we have
⇒ 511 = 7 × 73
⇒ 657 = 3 × 3 × 73
⇒ 146 = 2 × 73
⇒ HCF of 511, 657 and 146 = 73
Therefore, the greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively is 73.
