Number properties PS

[punitkaur]

For how many positive integers x is 130/x an integer?

a) 8 b) 7 c) 6 d) 5 e) 3

i dont have the OA. My answer is a, would like to confirm.

[grockit_jake]

Yes, you are correct. You can first break 130 into its factors, and then recombine to see how many fit.

130 = 2*65 = 2*5*13

2, 5, 13, 10, 65, 26, 130, 1.

Count your way up, and when you hit the max, you know you are done.

[punitkaur]

thanks for confirming. but the way i did it was a little different.
130
prime factors - 2,5,13.

no of divisors is multiplication of (powers of each +1)
2x2x2 = 8.

If we got a larger number then this method is easier I believe?

[tohellandback]

thanks for confirming. but the way i did it was a little different.
130
prime factors - 2,5,13.

no of divisors is multiplication of (powers of each +1)
2x2x2 = 8.

If we got a larger number then this method is easier I believe?

I think your method is better than one stated above..
the other method can be time-taking if there are large numbers.

[iships]

I usually get stuck in such "How many" questions,,,

[spartigrl]

How can you determine from the prime factors how many total factors there are?