IIT JEE , AIEEE Forum - Mathematics , Algebra - In how many different ways the no 1440be expressed as product of 2 factors

harsha_27

the proof comes under number theory ......u just remember the formula given below
if N is any natural no.
and N = [P1^A1][P2^A2][P3^A3].........[Pk^Ak]

then the no. of ways in which N can be resolved into product 2 factors is

1/2[A1+1][A2+1][A3+1].......[Ak+1] , if N is NOT a perfect square

=

1/2{ [A1+1][A2+1][A3+1].......[Ak+1] + 1} , if N is a perfect square

so for ur qn. the answer if u apply the formula above comes out to be
1/2[5+1][2+1][1+1]=1/2[36] = 18

Ask & Discuss Questions with Community & Experts