Question:The H.C.F of two numbers is 11 and their L.C.M is 693. If one of the numbers is 77, find the other.
Answer
The other number = `((11xx693)/77) = 99`
Question:The H.C.F of two numbers is 11 and their L.C.M is 693. If one of the numbers is 77, find the other.
The other number = `((11xx693)/77) = 99`
Question:Find the largest number that can exactly divide `513, 713` and `1107`.
Required number = H.C.F. of `513, 783` and `1107`. Now, `513 = 3^3 xx 19,` ` 783 = 3^3 xx 29,` and `1107 = 3^3 xx 41` `:.` H.C.F. = `3^3 = 27` Hence, the required number is `27`
Question:Find the greatest number which can divide 284, 698 and 1618 leaving the same remainder 8 in each case.
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`.
Question:Find the largest number which divides 62, 132 and 237 to leave the same reminder in each case.
Required number = H.C.F of (132-62), (237-132) & (237-62)
= H.C.F of 70, 105 & 175 = 35.Question:Find the largest number of four digits exactly divisible by 12, 15, 18 and 27.
The largest number of four digits is 9999. Required number must be divisible by 1 c.m of 12, 15, 18, 27 i.e. by 540. On dividing 9999 by 540, we get 279 as remainder. `:.` Required number = (9999-279) = 9720.