Trailing Zeros in 100!

CAT 1993 Slot 1 · QA · Medium · QA

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The product of all integers from 11 to 100100 will have the following numbers of zeros at the end.

  1. A.

    20

  2. B.

    24

  3. C.

    19

  4. D.

    22

Answer

B

Explanation

The number of trailing zeros in 100!100! is given by the exponent of 55 in 100!100!: ⌊1005⌋+⌊10025⌋=20+4=24.\left\lfloor \frac{100}{5} \right\rfloor + \left\lfloor \frac{100}{25} \right\rfloor = 20 + 4 = 24.

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