Question

find the greatest number which divides 319,572 and 1329 leaving remainders 4,5 and 6 respectively

Answer 1

The required number when divide 319, 572 and 1329 leaves remainder 4, 5 and 6.

Solution of this question is attached

Answer 2

(i)

To find the greatest number, we subtract 4,5 and 6 from 319, 572 and 1329.

⇒ 319 - 4 = 315

⇒ 572 - 5 = 567

⇒ 1329 - 6 = 1323.

(ii)

We have to find the HCF of those numbers.

⇒ Prime factorization of 315 = 3 * 3 * 5 * 7

⇒ Prime factorization of 567 = 3 * 3 * 3 * 3 * 7

⇒ Prime factorization of 1323 = 3 * 3 * 3 * 7 * 7

HCF(315,567,1323) = 3 * 3 * 7

                               = 63.

Therefore, Greatest number is 63.

Hope it helps!