Question

# Using Euclids division algorithm, find the largest number that divides $$1251, 9377$$ and  $$15628$$  leaving remainders $$1, 2$$  and $$3,$$ respectively.

Solution

## We have to find the H.C.F. of $$\left( 1251-1 =1250\right) , \left( 9377-2 =9375\right),\left( 15628-3 =15625\right),$$Find H.C.F of $$1250$$ and $$9375$$ :-$$9375=1250\times 7+625$$$$1250=625\times 2+0$$Since, remainder is $$0$$, the H.C.F is $$625$$Now, H.C.F of $$\left( 625,15625 \right)$$ is$$15625=625\times 25+0$$Hence $$625$$ is the H.C.F of all the three numbers and divides $$1251, 9377$$ and $$15628$$ leaving remainders $$1, 2$$ and $$3$$, respectively.Maths

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