If 60! is written out as an integer, with how many consecutive 0's will that integer end?
A) 6
B) 12
C) 14
D) 42
E) 56
OAC
Hi Experts ,
Please explain.
Many thanks in advance
SJ
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consecutive 0’s
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Hi jain2016,
There's a discussion of this question here:
https://www.beatthegmat.com/no-of-zeros- ... 77777.html
GMAT assassins aren't born, they're made,
Rich
There's a discussion of this question here:
https://www.beatthegmat.com/no-of-zeros- ... 77777.html
GMAT assassins aren't born, they're made,
Rich
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Matt@VeritasPrep
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We can phrase this question as
"How many 10s can be found in the factorization of 60! ?"
or, since 10 = 5 * 2 and 5s are less common than 2s,
"How many 5s can be found in the factorization of 60! ?"
Then we just count the factors of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.
The numbers in red count twice, since they contain 5*5. Counting those twice, we have a total of FOURTEEN 5's in the list above, and we're set!
"How many 10s can be found in the factorization of 60! ?"
or, since 10 = 5 * 2 and 5s are less common than 2s,
"How many 5s can be found in the factorization of 60! ?"
Then we just count the factors of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.
The numbers in red count twice, since they contain 5*5. Counting those twice, we have a total of FOURTEEN 5's in the list above, and we're set!
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Zeros as the end of a number means we are multiplying the number by powers of 10jain2016 wrote:If 60! is written out as an integer, with how many consecutive 0's will that integer end?
A) 6
B) 12
C) 14
D) 42
E) 56
OAC
Hi Experts ,
Please explain.
Many thanks in advance
SJ
We know that 10 = 5*2, this means a 10 has 1 power of 5 and one power of 2 in it.
Therefore if we have to calculate the number of 10s at the end, we need to calculate the number of powers of 5 in the number.
In the given number 60!,
Total powers of 5 = [60/5] + [60/25] = 12 + 2 = 14
Total powers of 2 = [60/2] + [60/4] + [60/8] + [60/16] + [60/32] = 20 + 15 + 7 + 3 + 1 = 46
Clearly the powers of 5 are less than the powers of 2. We need not calculate the powers of 2 as we know for sure that the powers of 2 would be higher than the powers of 5 in 60!
Hence the total number of 10s = 14
Number of zeors at the end = 14
Correct Option: C
