Question

Plzz help....
How many zeroes are there after 200! ?
Plz explain your answer.
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Answer 1

Answer:

8?

Step-by-step explanation:

because So, 200/25= 8, so we have eight more zeros. Lastly, 5^3= 125, and we have one such number in 200!, which gives us one more trailing zero. Therefore, we have 40+8+1=49 trailing zeros.

Answer 2

Note:

Number of zeroes are representation of number of pairs of (2 * 5 = 10) because 2 * 5 = 10 which makes one zero.

(i) Factors of 5:

⇒ Number of multiples of 5 in 200! = (200/5)

                                                            = 40{So,there are 40 zeroes}

(ii) Factors of 5²

⇒ Number of multiples of 5² in 200! = (200/25)

                                                             = 8.

(iii) Factors of 5³:

⇒ Number of multiples of 5³ in 200! = (200/125)

                                                             = 1

Therefore, Number of zeroes in the 200! =40 + 8 + 1 = 49.

Hope it helps