Question

Find the greatest number which divides 645and 792 leaving remainders 7and 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

Answer 2

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