How many factors of 6! are greater than 100?

Question

(A) 4
(B) 6
(C) 7
(D) 10
(E) 12

chetan2u · Answer

A good Q and not a very easy one ...

6! =1*2*3*4*5*6 = 2^4*3^2*5=720 
 now the trick is NOT to try and find the ONES greater than 100 BUT the ones that are required to be multiplied by factors above 100 to get 6! 
the lowest factors are 1,2,3,4,5,6 which can be seen from 6! if we check 6...  \frac{6!}{6}=2*3*4*5=120>100 
next will be 2*4=8 and  \frac{2*3*4*5*6}{2*4}=3*5*6=90<100 
so our answer is 1,2,3,4,5,6 so  6 values

Realized, missed out on 1....

Cezarel · Answer

6!= 6*5*4*3*2
What combination of numbers is over 100?
1. 6*5*4
2. 6*5*4*3
3. 6*5*4*3*2
4. 6*5*4*2
5. 6*5*3*2

Note: 5*4*3*2 is over 100, but it can be written as (3*2)*5*4, which is equal 6*5*4

Ans: B

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niks18 · Answer

6! = 6*5*4*3*2

Now number of factors that are greater than 100 are -

1) 6*5*4*3*2 = 720

2) 6*5*4*3 = 360

3) 6*5*4*2 = 240

4) 6*5*3*2 = 180

5) 6*4*3*2 = 144

6) 5*4*3*2 = 120

IMO number of factors should be 6 but there is no such option

Hi  Bunuel

Can you confirm whether the OAs are correct or point out the EXTRA factor in my method?

Bunuel · Answer

The OA is 6. Edited the options. Thank you.

EMPOWERgmatRichC · Answer

Hi All,

We're asked for the number of factors of 6! that are greater than 100. Since 6! is a relatively easy number to deal with, we can 'brute force' the solution by listing out the factors that are greater than 100:

(1)(720) 
(2)(360) 
(3)(240) 
(4)(180) 
(5)(144) 
(6)(120) 
(8)(90)

At this point, we can stop working. Each of the first 6 pairs has a factor greater than 100, but as the first number in each pair increases, the second number will decrease (thus, there's no reason to look at 'pairs' above 8 and 90).

Final Answer:  B; 6 factors

GMAT assassins aren't born, they're made, 
Rich

Shiva276 · Answer

Finding all factors for 720 (i.e 6!) above 100 implies the accompanying factor must be <8
Since 720/100 < 8
So we need to find all X that fulfills below conditions:
X*(7 or 6 or 5 or.. 1) = 720

From here on, we do a quick trial for each.
7 can't divide 720 so that's out.

The remaining digits 1 to 6 are All factors of 720, so therefore we'll have six values for X to satisfy that condition.

Hence Answer: 6

onlymalapink · Answer

what about 6x5x4 is that not valid?
it gives the same values but is clearly abdoggerent factor?

Kinshook · Answer

How many factors of 6! are greater than 100?

6! = 2^4*3^2*5=720

Factor greater than 100 = {720, 360, 180, 144, 240, 120}

IMO B

How many factors of 6! are greater than 100?

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How many factors of 6! are greater than 100?

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