find the greatest number which divides 632 and 2561 leaving remainder 7 and 11 respectively

Dear student,
On dividing 632 by the required number, remainder is 7
∴ 632-7 = 627 which will be exactly divided by the required number
Similarly,
2561-11=2550 will also be exactly divided by the required number
so the required number is HCF of 638 & 783
Prime factorization of 625 is 5 x 5 x 5 x 5 
Prime factorization of 2550 =2, 3, 5, 5, 17
HCF of 625 and 2550 is 5x5=25
∴ the required greatest number which divides 632 and 2550 leaving a remainder 7 and 11 respectively is 25
Regards

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