Compute the number of odd divisors of 112,000

My book did an example similar to this, but it was very vague. I didn't really understand where it came up with the numbers.

I think this one is giving me a hard time because I am using the trial and error algorithm--if there is such a thing--for getting a prime factorization. Does anyone have any tricks for getting a prime factorization?(Headbang)

Thanks.