240 is the smallest number with at least 19 factors. 240 has twenty factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240 262144 is the smallest number with EXACTLY 19 factors
It is actually 144
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
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.
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.
240 is the smallest number with at least 19 factors. 240 has twenty factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240 262144 is the smallest number with EXACTLY 19 factors
It is actually 144
30.
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16
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
16
The smallest number with exactly 36 factors is 1260. The factors are: 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, and 1260.
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.
Any prime number to the 14th power, like 16384.
Factors are numbers which divide another number exactly. The factors of 11 are 1 and 11. The factors of 15 are 1, 3, 5 and 15. So the only common factor of 11 and 15 is 1.
The smallest number that is divisible by 20 and 15 is 60.