Find the greatest number which divide 2300 and 3500 leaving 32 and 56 respectively as reminder.

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llltkl | College Teacher | (Level 3) Valedictorian

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Subtracting the corresponding remainders from 2300 and 3500 respectively, we get the two numbers as:

(2300-32) = 2268 and

(3500-56) =3444.

Now, the greatest number which divides 2300 and 3500 leaving 32 and 56 respectively as remainder will be the H.C.F of 2268 and 3444.

By factorizing 2268 = 2*2*3*3*3*3*7

and 3444 = 2*2*3*7*41

Hence the required H.C.F. of 2268 and 3444 is 2*2*3*7 = 84

Therefore, the greatest number which divides 2300 and 3500 leaving 32 and 56 respectively as remainder is 84.

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