Question

Find the highest power of 10 in 50!+60!+70! ?
10 की उच्चतम घात का पता लगाएं -50! +60! +70! ?
a)50
b)14
c)5
d)12
IM​

Answer 1

Highest power = 12.

Given that,

50!+60!+70!

=50! (1 + 51.52.53.54.55.56.57.58.59.60 + 51.52.53.54.55.56.57.58.59.60...70)

=50! (52.52.53.54.55.56.57.58.59.60 + 51.52.53.54.55.56.57.58.59.60...70)

=50! ×10(52.52.53.54.55.56.57.58.59.6 + 51.52.53.54.55.56.57.58.59.60...7)

=50! ×10(Odd + Even)

=50! ×10(Odd)

So, the highest power of 10 will be (1 + largest power of 10 in 50!)

To find highest power of 10 in 50!,

We need to find the number of the odd multiples of 10 and 5 in 50!

then the largest power of 10 in 50! will be = (no. of odd multiples of 10) + 2(no. of odd multiples of 5)

To find no. of odd multiples,

For 10 => 0

similarly,

For 5 => n=6,

So, Largest power of 10 in 50! = 12.

Hence, highest power of 10 in 50! +60!+70! = 12.

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