What is the smallest number that has exactly 12 factors?
211
60
120
144
Answers
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answer is 60
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Answer:
Step-by-step explanation:
What is a number that has 12 factors?
Originally Answered: What number has exactly 12 factors?
Since 12=22⋅3 the smallest answers involving the fewest prime numbers are:
211=2048
25⋅3=96
23⋅32=72
22⋅3⋅5=60
But you can get larger answers by substituting other primes for 2,3,5 in the above expressions.
By the way the twelve factors of 60 are: 1,2,3,4,5,6,10,12,15,20,30, and 60. The sum of the proper divisors is 78 which makes 60 an with abundance 18.
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Originally Answered: What number has exactly 12 factors?
There are infinitely many solutions to this, but they all fall into one of four classes of number.
The product of two primes and the square of a third. The smallest is 4 x 3 x 5 = 60
The product of the square and the cube of two primes. The smallest is 8 x 9 = 72
The product of one prime and the fifth power of another prime. The smallest is 32 x 3 = 96
The eleventh power of a prime. The smallest is 4096
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Originally Answered: What number has exactly 12 factors?
Another answer listed only prime numbers. I’m not sure if you re-wrote your question after that person answered, but I hope this answer suffices for your question as it is currently written.
72:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
#1: 72/1 = 72
#2: 72/2 = 36
#3: 72/3 = 24
#4: 72/4 = 18
#5: 72/6 = 12
#6: 72/8 = 9
#7: 72/9 = 8
#8: 72/12 = 6
#9: 72/18 = 4
#10: 72/24 = 3
#11: 72/36 = 2
#12: 72/72 = 1