100 followers special

IT WILL BE BETTER IF YOU CAN CHANGE YOUR STATEMENT; SUM OF FIRST HUNDRED INTEGERS TO SUM OF FIRST 100 NATURAL NUMBERS

SOLUTION:

(a) Number of factors of 100

=100 can be written as $2^{2}$ X $5^{2}$

=Therefore, no. of factors

="+1" the power of prime numbers

=(1+2)(1+2)

= $\boxed{9}$

(b)1+2+3.....+99+100

= $\frac{n(n+1)}{2}$

= $\frac{100(101)}{2}$

= $\boxed{5050}$

(c)no. of trailing zeros:

= $\frac{100}{5}$ = $\boxed{20}$

= $\frac{20}{5}$ = $\boxed{4}$

(divide any given positive integer repeatedly by 5 until it gets divided by it to find the no. of trailing zeroes.)

therefore, the answer is:

= $\boxed{9}$ + $\boxed{5050}$ + $\boxed{20}$ + $\boxed{4}$

= $\boxed{5083}$