Find the number of zeros at the end of 130.

Explanation

The number of zeros at the end of 130! Is equal to the exponent of 10 in 130. Now, exponent of 10 is equal to exponent of 5 as exponent of 2 is higher than exponent of 5. Now, exponent of 5 is
`[(130)/(5)]+[(130)/(5^(2))]+[(130)/(5^(3))]=26+5+1=32`
Also, exponent of 10 is 32, hence, there are 32 zeros at the end of 130. It should be noted that exponent of 2 is
`[(130)/(2)]+[(130)/(2^(2))]+[(130)/(2^(3))]+[(130)/(2^(4))]+[(130)/(2^(5))]+[(130)/(2^(6))]+[(130)/(2^(7))]`
=65+32+16+8+4+2+1=128
Hence, exponent of 10 is equal to exponent of 5.