Which of the following is a divisor of 12! · 6! + 12! + 6! + 1?
A. 21
B. 77
C. 91
D. 115
E. 143
Hint: Use Wilson's Theorem.
Please answer with solution, thanks in advance! :))
A. 21
B. 77
C. 91
D. 115
E. 143
Hint: Use Wilson's Theorem.
Please answer with solution, thanks in advance! :))
Add an Answer
More Questions From This User See All
Answers & Comments
Given :
To Find :
Solution :
12! · 6! + 12! + 6! + 1
= 12!(6! + 1) + (6! + 1)
= (12! + 1)(6! + 1)
= {(13 - 1)! + 1}{(7 - 1)! + 1}
As per Wilson's theorem, if n is prime number, (n - 1)! + 1 is divisible by n
Now, 13 and 7 are both prime numbers so the expression is divisible by both 7 & 13,
Hence, Option [C] is correct.
Verified answer
Answer:
12! · 6! + 12! + 6! + 1
Notice that you can factorise this:
6!(12! + 6!) + 1!(6! + 1)
12!(6! + 1) + 1(6! + 1)
(12! + 1)(6! + 1)
Therefore, using wilson's theorem, the number is divisible by either 13 or 7.
Now, 7 is divisible, 13 is divisible. Therefore, 7×13 = 91 also applies.
Therefore, C is correct.
⊱ ────── ✯ ────── ⊰
#CarryOnLearning