### "Fatness" of a Number

My girlfriend was being goofy and said that prime numbers were fat. I got to thinking and decided that she is wrong. Let an integer n be fatter than an integer m mean that n has more factors than m. Furthermore, let a number's "weight" or "fatness" be the number of positive factors of that number. For example:

30 is fatter than 15 since 30 has 8 factors and 15 only has 4. So:

1. What is the fattest number? How fat is it?

2. What is the skinniest number? How fat is it?

Ok, time to watch basketball.

30 is fatter than 15 since 30 has 8 factors and 15 only has 4. So:

1. What is the fattest number? How fat is it?

2. What is the skinniest number? How fat is it?

Ok, time to watch basketball.

## 1 Comments:

The skinniest integer will be zero, as it has no factors. The skinniest natural number will be one, as it has only one factor. There will be no fattest number, as, given any integer N, you can always find an integer with more factors (say by multiplying N by all of its factors and N + 1).

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