find the greatest number which can divide 284 698 and 1618, HCF & LCM, General Mathematics

Question:Find the greatest number which can divide 284, 698 and 1618 leaving the same remainder 8 in each case.

Answer Required number = 
H.C.F. of `(284 - 8), (698 - 8)` & `(1618 - 8)`
= H.C.F. of `276, 690` and `1610.`

Now, 
`276 = 2^2 xx 3 xx 23,`
`690 = 2 xx 3 xx 5 xx 23,` 
`1610 = 2 xx 5 xx 7 xx 23`

`:.` H.C.F. of `276, 690` & `1610` is `23`.
Hence, the required number is `23`.

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Find the greatest number which can divide 284, 698 and 1618 leaving the same remainder 8 in each case.

Question:Find the greatest number which can divide 284, 698 and 1618 leaving the same remainder 8 in each case.

Answer Required number = H.C.F. of `(284 - 8), (698 - 8)` & `(1618 - 8)` = H.C.F. of `276, 690` and `1610.` Now, `276 = 2^2 xx 3 xx 23,` `690 = 2 xx 3 xx 5 xx 23,` `1610 = 2 xx 5 xx 7 xx 23` `:.` H.C.F. of `276, 690` & `1610` is `23`. Hence, the required number is `23`.