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Using Euclid's division algorithm, find ...

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

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Numbers for H.C.F are
1251 -I, 9377 -2 and 15628 -3= 1250, 9275 and 15625
For the numbers 15625 and 9375
By Euclid's division algorithm
`15625 =9375 xx1+ 6250`
`9275 =6250xx 1+3125`
`6250 =3125xx 2+0`
`:.H.C.F. (15625, 9375)=3125`
Again for numbers 1250 and 3125
By Euclid's division algorithm
`3125 =1250xx2+625`
`1250 =625 xx 2+0`
`:.H.C.F. (3125 ,1250 )=625`
Hence , `H.C.F. (15625, 9275 , 1250 )=625`
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