Nikkz99 wrote:
Crytiocanalyst wrote:
Bunuel wrote:
If \(n! = n*(n - 1)*(n - 2)*...*1\), where n is a positive integer, which of the following is (are) true?
I. 26 is not a factor of 25!
2*13 is a factor of 25!
II. 29 is a factor of 25!
29 is a prime number and only happen if till 29! happens therefore not a factor
III. 1,000,000 is a factor of 25!
Yes since 5^6 is a factor and 2^19 is a factor
Therefore IMO B
Can someone debrief like how 2X13 is a factor of 13? How 2^19 and 5^6 factor ?
OR can someone attach me reference for this topic?
Thank you.
If \(n! = n*(n - 1)*(n - 2)*...*1\), where n is a positive integer, which of the following is (are) true?
I. 26 is not a factor of 25!
II. 29 is a factor of 25!
III. 1,000,000 is a factor of 25!A. None
B. III Only
C. I and II only
D. II and III only
E. I, II, and III
I. 26 is not a factor of 25!
Since 26 = 2*13 and 25! contains both of these factors (25! = 1*2*...*13*...*25), then 26 IS a factor of 25!. Thus, the above statement is not true.
II. 29 is a factor of 25!
Since 29 is a prime number and 25! contains only the prime numbers up to 25, then 29 is NOT a factor of 25!. Thus, the above statement is not true.
III. 1,000,000 is a factor of 25!
The number of trailing zeros of 25! is calculated by 25!/5 + 25!/25 = 5 + 1 = 6 (check here for more:
https://gmatclub.com/forum/everything-a ... 85592.html). Hence, 10^6 is indeed a factor of 25!. Thus, the above statement IS true.
Answer: B.
For more:
12.
Trailing Zeros13.
Power of a number in a factorialHope this helps.