power

[gmatblood]

What power of 8 exactly divides 25!

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

[saketk]

What power of 8 exactly divides 25!

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

You just have to find the exponent of 8 in the product till 25.

count all even and separate the 2's. Club them into the power of 3 and you will have your answer.

It should be 7

[rijul007]

First find out what power of 2 exactly divides 25!

In first 25 nos.. you have
12 nos divisible by 2
6 nos divisible by 4
3 nos divisible by 8
1 no divisible by 16

Total power 22

2^22 exactly divides 25!

8^7 * 2

So the ans is 7

Option C

[saketk]

This is what I meant...

[spoiler]2*4*2*8*2*4*2*4*4*2*4*2*4*2 = 2^74^6*8

8*8*8*8*8*8*8*2 = 7 times 8[/spoiler]

[shankar.ashwin]

2 | 25
2 | 12-1
2 | 6 - 0
2 | 3 - 0
2 | 1 -1

Total - 12+6+3+1 = 22. Now 8 has 3 2's. So 22/3 ~ 7

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I am still not clear about the explanation please reply in detail ......

[kdraj]

I am not sure if there is quick way to find it in within 30 seconds as this is a straight forward problem. The way I did was.

25.24.23.22.21.20.19.18.17.16.15.14.13.12.11.10.9.8.7.6.5.4.3.2.1

Count the number of 2's in each of the number above. Divide the number by 3 -> gives you the number of 8s

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ya...got it now...

easiest way...thanks !!!!!!

[LalaB]

write down all numbers with 2 -

2;4;6;8;10;12;14;16;18;20;22;24

then we have -

1.2(1 two);4(2 twos) that is eight
2.8
3.10(1 two);12 (1 four)
4.14;16
5.16;6
6.18;20
7.22;24

so , the answ is 7