Question

No. of zeros at the end of (45!)*10

Answer 1

maximum pair of 2 and 5 that can be made are 10 so the number of zeros at the end of the 45! is 10.

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Hope it helps you.

Answer 2

Given :- Number of zeros at the end of (45!) * 10 .

Solution :-

As we know that,

• 0 in last is by 2 * 5 .
• so, in order to find total zeroes in last we have to check how many times 5 was there in the factorial .{ since 2 comes most times we will go for less numbers. }

then,

→ Total 5's in 45! = (5, 2*5, 3*5, 4*5 , 5*5, _____ 9*5) = 9 + 1 = 10 . { since in 25 , 5 is multiply 2 times. }

therefore,

→ Total zeroes at the end of 45! = 10 .

hence,

→ Total zeroes at the end of 45! * 10 = 10 + 1 = 11 (Ans.)

Shortcut :-

Total number of zeroes in 45! :-

Dividing factorial value by 5,

→ 45/5 = 9 Quotient .

now, dividing quotient by 5 again,

→ 9/5 = 1 Quotient .

since 1 < 5.

→ Total number of zeroes at the end of 45! = sum of quotients = 9 + 1 = 10 .

therefore,

→ Total zeroes at the end of 45! * 10 = 10 + 1 = 11 (Ans.)

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