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Well, isn't that a happy little question! The smallest number with 16 factors is 60. You see, when you break down 60 into its prime factors (2, 2, 3, 5), you can use the formula (a+1)(b+1)(c+1)... where a, b, c are the exponents of the prime factors to find the total number of factors.
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ProfessorThe smallest number with 16 factors is determined by considering the prime factorization of the number. Since the number of factors is related to the exponents of the prime factors, we need to find a number with a prime factorization that allows for 16 factors. To achieve this, we can start with the prime factorization of 2^3 * 3^2, which results in (3+1)(2+1) = 12 factors. To reach 16 factors, we can multiply this by another Prime number raised to the power of 1, resulting in 2^3 * 3^2 * 5^1 = 360.
Oh, dude, the smallest number with 16 factors is 60. Yeah, it's like a little math puzzle, but don't worry, I got you covered. So, 60 has factors like 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. That's 12 factors, and then you also have the negative versions of those numbers, adding up to 16 factors in total. Math can be fun, right?
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What is the smallest number with only five factors?
16
What is the smallest number with nineteen factors?
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
What is the smallest number that has 4 different prime factors?
The smallest prime factors are 2,3,5,7 thus the smallest number would be the product of these will be 210
What number has 20 factor and it the smallest number?
240 is the smallest number with twenty factors.
What is the least positive integer that has exactly 13 factors?
4096 is the smallest number with exactly 13 factors. (Including 1 and itself as factors).192 is the smallest number with exactly 13 properfactors, (excluding the number itself).120 is the smallest number with at least 13 factors (it has 16 factors)To find the smallest number with exactly N factors (for example, N=12):Factor N into primes, (for example, 12= 2*2*3Subtract 1 from each of the prime factors (for example, 1,1,2)Sort them by largest first (for example, 2,1,1)Raise successive prime numbers to these powers (for example, 2^2,3^1,5^1)Multiply these together (for example: 4*3*5 = 60; 60 is the smallest number with exactly 12 factors).
