(Q). Find the highest power of 10 in 10! + 20! + 30! + 40! + 50! + 60! + 70! +80! + 90! + 100! + 110! + 120!.
Solution:-
From earlier question we know that highest power of 10 in multiplication of theser factorials is 182. Now herefactorials are written in summation form. Hence we have to find the highest power of 10 or in other words number of trailing zeros in the factorial summation.
As the value of factorial number increases, the number of trailing zeros at its end will also increases. Hence out of these 10! which has least number of trailing zeros at its end & all other factorials will have more number of trailing zeros than 10!
Hence highest power of 10 = number of trailing zeros in the summation = highest power of 10 in 10! ➡