The remainder of (3)67! divided by 80 is :
A. 0
B. 1
C. 2
D. 3
E. 4
Answer: Option B
Solution(By Examveda Team)
Since, $${3^4} = 81$$ gives remainder 1 on divided by 80So, $$\frac{{{3^{4n}}}}{{80}}$$ gives remainder 1
Thus, $$\frac{{{3^{67!}}}}{{80}}$$ will also give the remainder as 1
Since, 67! = 4n for a positive integer n
This Question Belongs to Arithmetic Ability >> Number System
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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
We always have, 3^4 = 81 == 1 mod 80. Hence, for any positive integer n, we have, 3^(4^n )=1 mod n. Hence, the answer is option B.
By Sanjay Mohan Bhatnagar (www.mathsacad99.com)