What is the remainder when 461 is divided by 51 ?
A. 20
B. 41
C. 50
D. None of these
Answer: Option D
Solution(By Examveda Team)
461 = 4 × 460 = 4 × (44)15 = 4 × (256)15Now, (xn - an) is divisible by (x - a) for all values of n.
∴ (25615 - 1) is divisible by (256 - 1) i.e., 255 and hence by 51
⇒ On dividing (256)15 by 51, we get 1 as remainder
⇒ On dividing 460 by 51, we get 1 as remainder
⇒ On dividing 461 by 51, remainder obtained = (4 × 1) = 4
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Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
Great