The number that has exactly 15 factors is 28. To determine the number of factors a number has, you can prime factorize the number and then add 1 to each exponent in the prime factorization and multiply these numbers together. In the case of 28, the prime factorization is 2^2 * 7^1, so the number of factors is (2+1) * (1+1) = 3 * 2 = 6. To have exactly 15 factors, the number needs to be a square of a Prime number, so 28 = 2^2 * 7^1 fits this criteria.
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This number would have to be a squared number as it only has 15 factors. The number I have calculated is 324 as the square root is 18
A prime number has exactly two factors.
15 has more than exactly two factors (1, 3, 5, and 15), therefore it is composite. 17, 19, and 23 each have exactly 2 factors (1 and the number itself), so they are primes.
A number has exactly three factors if and only if it is the square of a prime number.
The greatest common factor is the highest number that divides exactly into two or more numbers. Factors are numbers you can multiply together to get another number. Therefore, the common factors of 15 and 25 are 5 and 1.