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 = (11×69377)=99Question: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 = (11×69377)=99Question:Find the largest number that can exactly divide 513,713 and 1107.
Required number = H.C.F. of 513,783 and 1107. Now, 513=33×19, 783=33×29, and 1107=33×41 ∴ H.C.F. = 33=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=22×3×23, 690=2×3×5×23, 1610=2×5×7×23 ∴ 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.