Find the greatest number which divides 645 and 792 leaving a remainder 7 and 9 respectively
Answers
Answered by
36
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
∴ 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
Similar questions