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If P is the product of the integers from 2 to 40, what is the number 29 Dec 2020, 08:51
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

67% (01:06) correct 33% (01:30) wrong based on 93 sessions

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If P is the product of the integers from 2 to 40, what is the number of zeros that P ends with?

A. 12

B. 11

C. 10

D. 9

E. 8
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D
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If P is the product of the integers from 2 to 40, what is the number 29 Dec 2020, 09:00
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Abhi077
If P is the product of the integers from 2 to 40, what is the number of zeros that P ends with?

A. 12

B. 11

C. 10

D. 9

E. 8
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\(P = 40!\) , thus we are asked to find no of trailin zeros tin \(40!\)

\(\frac{40}{5} = 8\)
\(\frac{8}{5} = 1\)

So, Total no of zeros that P ends with is 9, Answer must be (D) 9
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If P is the product of the integers from 2 to 40, what is the number 30 Dec 2020, 11:21
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Abhishek009

\(P = 40!\) , thus we are asked to find no of trailin zeros tin \(40!\)

\(\frac{40}{5} = 8\)
\(\frac{8}{5} = 1\)

So, Total no of zeros that P ends with is 9, Answer must be (D) 9
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Can you explain why you divide by 5? Thanks!
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If P is the product of the integers from 2 to 40, what is the number 30 Dec 2020, 14:52
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Solution



Given
In this question, we are given that
    • P is the product of the integers from 2 to 40
      o It means P = 40!

To find
We need to determine
    • The number of zeros that P ends with

Approach and Working out
The zeros at the end of a factorial value are produced by a combination of 2 x 5.
Also, for any factorial value, the number of 5s will be always less than the number of 2s.
    • Hence, we need to calculate only the number of 5s in 40!
    • 5s present in 40! = 40/5 + 40/25 = 8 + 1 = 9

Thus, option D is the correct answer.

Correct Answer: Option D
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If P is the product of the integers from 2 to 40, what is the number 31 Dec 2020, 08:34
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Abhishek009

\(P = 40!\) , thus we are asked to find no of trailin zeros tin \(40!\)

\(\frac{40}{5} = 8\)
\(\frac{8}{5} = 1\)

So, Total no of zeros that P ends with is 9, Answer must be (D) 9

Can you explain why you divide by 5? Thanks!
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We get a 0 as a consequence of the product of 2 and 5. Any factorial, will have more 2's than 5's.

For eg. 5! = 5 * 4 * 3 * 2 * 1 = 5 * (2 * 2) * 3 * 2 * 1. So there is 1 five and 3 twos.

Therefore to find trailing 0's , we divide that number by 5. If the quotient obtained is ≥ 5, then redivide. the number of trailing 0's is the sum of the quotients. Please note that we do not worry about the remainders. for eg 100!

So 100/5 gives a quotient of 20. Since 20 is > 5, we now divide the quotient by 5. We get 20/5 = 4

Since 4 is < 5 our answer is 20 + 4 = 24.


Hope this helps

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If P is the product of the integers from 2 to 40, what is the number 27 Aug 2023, 20:39
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