Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.


Since, 1, 2 and 3 are the remainders of 1251, 9377 and 15628 respectively. Thus after subtracting these remainders from the numbers , we get


1251 – 1 = 1250, 9377 − 2 = 9375 and 15628 − 3 = 15625 which is divisible by the required number.


Now, required number = HCF (1250, 9375, 15625)


By Euclid’s division algorithm, b = a × q + r, 0 ≤ r < a


Here, b is any positive integer .


Firstly put b = 15625 and a = 9375


15625 = 9375 × 1 + 6250


9375 = 6250 × 1 + 3125


6250 = 3125 × 2 + 0


So, HCF (9375, 15625) = 3125


Now, put a = 1250 and b = 3125


3125 = 1250 × 2 + 625


1250 = 625 × 2 + 0


So, HCF (1250, 3125) = 625


Hence, 625 is the largest number which divides 1251, 9377 and 15628 leaving remainder 1, 2 and 3, respectively.


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