Question

Find the no. of zeroes at the end of 50! ​

Answer 1

$\huge\star{\tt{\underline{\underline{\red{Answer}}}}}\star$

#Zeroes can be obtained from 2 and 5

Exponent of 2 in 50! = $\bigg[\frac{50}{2}\bigg]$ +$\bigg[\frac{50}{4}\bigg]$ +$\bigg[\frac{50}{8}\bigg]$ +$\bigg[\frac{50}{16}\bigg]$ +$\bigg[\frac{50}{32}\bigg]$ +$\bigg[\frac{50}{64}\bigg]$

#Note:

[.] is G.I.F

$\implies$ 25+ 12 +6+3+1+0

$\implies$ $\bold{\boxed{\boxed{47}}}$

Exponent of 5 in 50! =$\bigg[\frac{50}{5}\bigg]$ +$\bigg[\frac{50}{25}\bigg]$ + $\bigg[\frac{50}{125}\bigg]$

$\implies$ 10+2+0

$\implies$ $\bold{\boxed{\boxed{12}}}$

We know that

we will always have to take the small number

so $\huge{\boxed{\boxed{12}}}$

Answer 2

Answer:

if counting from 0-50 then no. of zeroes are 6

if counting from 1-50 then no. of zeroes are 5

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