The number that has only three factors between 12 and 40 is 16. The factors of 16 are 1, 2, 4, 8, and 16. Since 16 has only three distinct factors (1, 2, and 4), it meets the criteria specified.
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If factors include 1 and the number itself then the any number (n) with only 4 factors has to be the product of two prime numbers, p1 and p2. The factors are then n, p1, p2, and 1. The largest 3-digit number with only 4 factors is 998. The factors are 998, 499, 2 and 1
A number that has only two factors is called a prime. The only factors of a prime are 1 and the number itself.
The way to be sure you have one of these is to take any three distinct prime numbers and multiply them. Those three prime numbers are then the only factors the product can have. An example is the number 30, which has factors of 2, 3 and 5.
For a number to have [only] 2 factors, it must be a prime number; the prime numbers between 0 and 20 are; 2, 3, 5, 7, 11, 13, 17, 19
Only perfect squares can have an odd number of factors. The answer is 16. It has five factors: 1,2,4,8,16.