Question

The last 3 digits in 10! are

Answer 1

In 10!

exponent of 5 is $=\left[\frac{10}{5}\right]+\left[\frac{10}{5^2}\right]+...$

$=2$

exponent of 2 is $=\left[\frac{10}{2}\right]+\left[\frac{10}{2^2}\right]+\left[\frac{10}{2^2}\right]+...$

$=5+2+1=8$

$\Rightarrow 5^2\times 2^2=100$ will male tusogeroes at the end

Now calculating the third digit. from

remaining numbers that are

Last digit $=1\times 3\times 4\times 6\times 7\times 8\times 9=3\times 4\times 6\times 7\times 2$

$=2\times 6\times 4=2\times 4=8$ [multiplying only last digit]

$\Rightarrow$ 3rd last = 8

$\Rightarrow$ Last 3 digits are 800