How many zeros are the end of ?

Question

How many zeros are at the end of  380!  ?

(A) 90
(B) 91
(C) 94
(D) None
(E) 95

In order to find the number of zeros we have to find out the number of 5's and 2's , because no. of 5's will be less then the number of 2's ..

Bunuel · Accepted Answer

380! has \frac{380}{5}+\frac{380}{5^2}+\frac{380}{5^3}=76+15+3=94 trailing zeros ( take only the quotient into account). Answer: C. For more on trailing zeros check: everything-about-factorials-on-the-gmat-85592.html Similar questions to practice: if-60-is-written-out-as-an-integer-with-how-many-101752.html how-many-zeros-does-100-end-with-100599.html find-the-number-of-trailing-zeros-in-the-expansion-of-108249.html find-the-number-of-trailing-zeros-in-the-product-of-108248.html if-n-is-the-product-of-all-multiples-of-3-between-1-and-101187.html if-m-is-the-product-of-all-integers-from-1-to-40-inclusive-108971.html if-p-is-a-natural-number-and-p-ends-with-y-trailing-zeros-108251.html if-10-2-5-2-is-divisible-by-10-n-what-is-the-greatest-106060.html p-and-q-are-integers-if-p-is-divisible-by-10-q-and-cannot-109038.html question-about-p-prime-in-to-n-factorial-108086.html if-n-is-the-product-of-integers-from-1-to-20-inclusive-106289.html what-is-the-greatest-value-of-m-such-that-4-m-is-a-factor-of-105746.html if-d-is-a-positive-integer-and-f-is-the-product-of-the-first-126692.html if-10-2-5-2-is-divisible-by-10-n-what-is-the-greatest-106060.html Hope it helps.

rever08 · Answer

380/5 = 76

76/5= 15

15/5= 3

Sum of these quotients. Answer C

rnz · Answer

How do you know how many times you need to add the fractions?

Bunuel · Answer

This is explained in highlighted post.

Abhishek009 · Answer

\frac{380}{5} = 76 
 \frac{76}{5} = 15 
 \frac{15}{5} = 3

So, the total number of 0's in the end of  380!  is 76+15+ 3 = 94 ,   answer will be (C)

Russ19 · Answer

Is there any good tip to have the result of the division (380/5^2=15) in an easier way?

Thanks for any response.

MHIKER · Answer

The basic formula for that is:  \frac{380}{5}+\frac{380}{5^2}+\frac{380}{5^3}; 5^4  is larger than 380.

=76+15+3=94

The answer is C.

Another way, considering the basic formula:
380/5=76
76/5=15
15/5=3

76+15+3=94

AnirudhaS · Answer

\frac{380}{5}+\frac{380}{25}+\frac{380}{125} 
=76+15+3 (not considering the remainders)
=94
Answer:  C

bumpbot · Answer

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How many zeros are the end of ?

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How many zeros are the end of ?

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