= H.C.F. of 48, 92 and 140 = 4.
Required H.C.F. = | H.C.F. of 9, 12, 18, 21 | = | 3 |
L.C.M. of 10, 25, 35, 40 | 1400 |
By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by 99.
Given Exp. = 666 x | 1 | x | 1 | = 37 |
6 | 3 |
Then, | n | [2a + (n - 1)d] = 1800 |
2 |
⟹ | n | [2 x 6 + (n - 1) x 6] = 1800 |
2 |
⟹ 3n (n + 1) = 1800
⟹ n(n + 1) = 600
⟹ n2 + n - 600 = 0
⟹ n2 + 25n - 24n - 600 = 0
⟹ n(n + 25) - 24(n + 25) = 0
⟹ (n + 25)(n - 24) = 0
⟹ n = 24
Number of terms = 24.
∴ H.C.F. of given numbers = 0.18.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
∴ Required number (9999 - 399) = 9600.
Then, their L.C.M. = 6x.
So, 6x = 48 or x = 8.
∴ The numbers are 16 and 24.
Hence, required sum = (16 + 24) = 40.
84 = 22 x 3 x 7
∴ H.C.F. = 22 x 3 = 12.
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