Question

find the largest positive number that divides 398,436,542 leaving remainder 7,11,15 respective ​

Answer 1

Answer:

17

Step-by-step explanation:

398-7=391

436-11=425

542-15=527

largest number that divides 398, 436 and 542 leaving remainder 7, 11 and 15 respectively = H.C.F of 391, 425 and 527.

Factor forms of each number are

391=17× 23

425=5×5× 17

527=17× 31

H.C.F of 391, 425 and 527 is 17.

Hence, the largest number which divides 398, 436 and 542 leaving remainder 7, 11 and 15 respectively is 17.

Answer 2

Answer:

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 )

Step-by-step explanation:

First deduct the remainders from each term

398 - 7 =391

436–11 = 425

542–15 =527

Next find the HCF of the terms that you get

391 = 17x23

425 = 5x5x17

527 = 17x31

The HCF is 17.

The answer is the HCF or 17.

Check 398/17 = 23 + 7 remainder

436/17 = 25 + 11 remainder

542/17 = 31 + 15 remainder