Data Sufficiency

If d is a positive integer, and f is the product of the first 30 positive integers, what is the value of d?

(1) 10^d is a factor of f
(2) d>6

OA is C

Can someone kindly explain whY?

Grazie mille

f is the product of first 30 numbers.
This product will have 7 zeros (Zero comes in the product when any number is multiplied by 10,20 and 30 and any even number is multiplied by 5, 15 and 25)

so we have

5 x 2 = 10
then the number 10
15 x 6 = 90
then the number 20
25 x 4 = 100
then the number 30

So altogether f has 7 zeros.

1) Says 10^d is a factor of f. 10 (d=1), 100 (d=2), 1000 (d=3), 10000 (d=4)...etc upto 10^7 can be a factor of f. Hence not sufficient.

2) Says d > 6. d can be any positive integer greater than 6.

Both combined, we have d = 7. Hence sufficient

Alara533 wrote:f is the product of first 30 numbers.
This product will have 7 zeros

I still don't understand why this product will have 7 zeros. Could you please elaborate on how this happens?

tuscan21 wrote:

Alara533 wrote:f is the product of first 30 numbers.
This product will have 7 zeros

I still don't understand why this product will have 7 zeros. Could you please elaborate on how this happens?

f = 30!

the numbers in 30! that produce a zero at the end are
2*5*10*12*15*20*22*25*30 = 594x10^7

ssmiles08 wrote:

tuscan21 wrote:

Alara533 wrote:f is the product of first 30 numbers.
This product will have 7 zeros

I still don't understand why this product will have 7 zeros. Could you please elaborate on how this happens?

f = 30!

the numbers in 30! that produce a zero at the end are
2*5*10*12*15*20*22*25*30 = 594x10^7

Why "10" for instance and not "11"?