que1> Find Number Of Zero's In The Expansion Of 79!?

que2>find Last Two Digit Of 95!?

do Snd The Method Also To Solve These Prob ?

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- May 5th 2008, 12:05 PMspeedtijoNeed Help With Basic Prob
**que1> Find Number Of Zero's In The Expansion Of 79!?**

**que2>find Last Two Digit Of 95!?**

**do Snd The Method Also To Solve These Prob ?** - May 5th 2008, 12:29 PMSoroban
Hello, speedtijo!

Quote:

1) Find the number of zero's in the expansion of

Consider the number: .

The question becomes: how many 5's are in the factorization?

(Since "5 times an even number" produces a 0.)

Every fifth number has a 5: .

. . There are fifteen 5's among the factors.

But a few of them__two__5's . . . these are the multiples fo 25.

. . There are: . of them.

Each of these contribute an addition 5 to the factoring.

Hence, there are: . factors of 5.

. . Each of them, paired with a factor 2, produces a 10.

Therefore, has eighteen 0's*at the end.*

Quote:

2) Find the last two digits of

Multiplying by 80, 81, 82, 83, ... 95, we get even more zeros at the end.

Obviously, the last two digits are 00.