The Prime Factorisation of 560 is: $560 = 2^4\times5\times7$

Each factor of 560 can either have no factors of 2, 1 factor of 2, 2 factors of 2, 3 factors of 2, or 4 factors of 2, so there are 5 possibilities. There could either be 1 factor of 5 or no factors of 5 so there are 2 possibilities. There is either 1 factor of 7 or no factors of 7, so there are 2 possibilities. So there are $5\times2\times2 = \boxed{20}$ factors of 560

560 can be written as 2^4 * 5 * 7, then the divisora are given by (e1+1)(e2+1)(e3+1) with e1, e2, e3 the exponentes of 2, 5 and 7 respectively. Then, we have 5 2 2=20 and this is the number of divisors

factorise 560 in powers of primes and then add 1 to the powers and multiply them

i wrote a program in c++

include<iostream.h>

include<conio.h>

void main() { clrscr(); int i,c=0,n; cout<<"enter no"; cin>>n; for(i=n;i>0;i--) { if(n%i==0) { c++; } } cout<<c; getch(); }

List out!! :)