Question

Find the greatest number which divides 645 and 792 leaving remainder 7 and 9 , respectively.

Answer 1

Answer:

On dividing 645 by the required number, remainder is 7

∴ 645-7 = 638 which will be exactly divided by the required number

Similarly,

792-9 = 783 will also be exactly divided by the required number

so the required number is HCF of 638 & 783

Prime factorization of 638 = 2x11x29

Prime factorization of 783 = 3x3x3x29

HCF of 638 & 783 = 29

∴ the required greatest number which divides 645 and 792 leaving a remainder 7 and 9 respectively is 29