How many positive integers N are there such that the least common multiple of N and 1000 is 1000?
I did found the solution to this problem , but I did it by brute force. When I was tackling this problem, I didn't know what multiples where so I had to look it up. I think I had a blurred view of what multiples are. So, to help me, I found the definition: multiples are some number multiplied by an integer. For instance, the multiples of 4 are ...-8,0,4,8,12,16,20 and so on.
And the least common multiple of 4 and 5(as in an example to help clarify the problem) is 20 because
The multiples of 4: 4,8,12,16,20
The multiples of 5: 5,10,15,20,25
I know I probably wasted your time writing that stuff above, but it helps me because I get forget what it means to find multiples.
Now back to the problem. The problem asks to find all values n such that 1000 is divisible by n. So basically, I just listed them like this:
n: 1 2 ,4, 5, 8, 10, 20, 25, 40, 50,100,125,200,250,500,1000
1000/n has remainder 0? : There are 16 n's.
So again, I feel like there's a trick or method in the problem that I don't know in order to solve the problem. Do you know any other way,besides my brute force method, in solving this problem?