0
4096 is the smallest one. Since the number of factors depends on the exponents of the prime factors, plus one, multiplied together, the set of numbers that meets the requirements are of the form:
p12, where p is a Prime number.
Still curious? Ask our experts.
Chat with our AI personalities
Maxine
Rafa
BeauAdd your answer:
Earn +20 pts
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).
What number is greater than 150 and has exactly three different factors?
Any square of a prime number 13 or greater, like 169.
A number that has exactly two factors?
A prime number has exactly two factors.
What numbers with exactly 3 factors are?
A number has exactly three factors if and only if it is the square of a prime number.
Is 143 composite?
143 is composite because it has more than 2 factors. Any number with exactly 2 factors (1 and the number itself) is prime. The factors of 143 are 1, 11, 13, and 143.
