Question

Find the number of zeros at the end of the product
35x36x37x - -- *89X90​

Answer 1

Question :--- Find the number of zeros at the end of the product 35x36x37x - -- *89X90 ?

Note :-- You want to know how many factors of 10 that is (5x2) you have.

There are plenty of even numbers, so you just need to see how many times 5 will come ..

→ In order for the product of some numbers to end in a zero, the prime factors of the numbers must include at least one 2 and one 5 since 5 x 2 = 10.

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Solution :---

we have to check How many Times 5 will come, that will be our answer for Number of zeros ?

→ 5 comes one times in = 35, 40, 45, 55, 60, 65, 70, 80, 85, 90 = Total 10 Times.

→ 5 comes Two times in = 50 and 75 = 2 + 2 = 4 Times .

( Reason :- 50 = 2*25 = 2*5*5 , and 75 = 3*25 = 3*5*5 , so, here 5 will come 2 times . )

So, Total Number of 5 will be = 10 + 4 = 14 Times .

Hence, Number of Zeros at the end of 35x36x37x - -- *89X90 will be 14 zeros....

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Practice Question For you now :- Find the number of zeros at the end of 1*2*3*4*5 ____________ 100 ?

Answer is 24 . ( Try Yourself now) .