a number that is greater than 301 that has an odd number of factors?

Answer 1

Tim GNO is wrong.

17 * 29 * 31 = 10013 has more than 3 factors. The factors of 10013 are 1, 17, 29, 31, 493, 527, 899, and 10013. As was mentioned above, only perfect squares have an odd number of factors. Reason is simply. Any factor of a number has a "co-factor". For example, 9 is a factor of 45, and its co-factor is 5 (since 9 * 5 = 45).

Since factors occur in cofactor pairs, there is always an even number of factors, UNLESS one of those cofactor pairs is made up of the same number twice, which by definition makes the original number a perfect square.

Answer 2

The only numbers that have an odd number of factors are perfect squares. So start looking for a perfect square greater than 301.

Hope this helps. :)

Answer 3

Thanks for your question! If you had asked for "a number with an odd number of prime factors", we could "think up" three (an odd number of) prime factors, which multiply together to produce a number greater than 301.

Suppose we choose the following three prime factors:

17, 29 and 31

Multiply them together:

17 * 29 * 31 = 10013

However, your question did not specify PRIME factors, in which case the first answerer is correct ... a perfect square S can be said to have "an odd number of factors" because S itself is one of its own factors.

Hope this helps.

Answer 4

The only integers that have an odd number of
factors are squares. The smallest one greater
than 301 is 18² = 324.

Answer 5

All square numberss have an odd number of factors, because one of the pairs of factors is the same number (e.g. 4x4=16). So, you have lots of choices.

Answer 6

I'm not sure what my factors are anymore.