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The greatest number that divides 411, 684, 821 and leaves 3, 4 and 5 as remainders, respectively, is
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- 254
- 146
- 136
- 204
Correct Option: C
We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of 411 – 3 = 408; 684 – 4 = 680 and 821 – 5 = 816
HCF of 408 and 816 = 408
HCF of 408 and 680
∴ Required number = HCF of 408 and 680
Hence , Required number = 136
