Question

Find the largest positive integers that will divide 398,436and 542 leaving remainder 7,11 and 15 respectivly

Answer 1

Answer :-

→ 17 .

Step-by-step explanation :-

We have ,

→ The number 398, 436 and 542 which when divides by a positive integers leaves remainder as 7, 11, and 15 respectively .

→ Clearly, the required number divides ( 398 - 7 ) = 391 , ( 436 - 11 ) = 425, and ( 542 - 15 ) = 527 exactly .

•°• Required number = HCF( 391, 425, 527 ) .

Now,

→ 391 = 17 × 23 ,

→ 425 = 5² × 17 ,

→ 527 = 17 × 31 .

$\therefore$ HCF( 391, 425, 527 ) = 17 .

Hence, the required number is 17 .