What is the greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 73
Given that
The greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively
According to the question
⇒ 554 - 43 = 511 = 7 * 73
⇒ 714 - 57 = 657 = 3 * 3 *73
⇒ 213 - 67 = 146 = 2 * 73
The integer number is exactly divided by 511, 657, 146
Hence, the greatest possible integer is HCF of (511, 657, 146)
= 73