0
The smallest positive integer with exactly 12 factors is 60.
You may check to see that 60 has exactly twelve factors, by noting the following:
60 = 1 X 60 = 2 X 30 = 3 x 20 = 4 X 15 = 5 x 12 = 6 x 10. The factors that are less than 8 are 1, 2, 3, 4, 5, and 6; the factors that are more than 8 are obtained by dividing the six factors already found into 60.
Any number less than 60 must have six numbers less than 8 that divide into it, in order to have exactly twelve divisors. In fact, the requirement is more stringent than that: for a number (n, say) to have exactly twelve divisors, six of them must be less than the square-root of n. That you won't be able to find any is borne out by the fact that the least common multiple of any 6 of the first seven integers must be at least as great as the l. c. m. of the first six positive integers, namely 60.
Still curious? Ask our experts.
Chat with our AI personalities
Coach
Devin
MaxineAdd your answer:
Earn +20 pts
What is the smallest number that is a multiple of 13 and is also divisible by 4 and by 6 with zero remaining?
I BELIEVE IT IS 156 THE SMALLEST NUMBER 4 AND 6 GO INTO IS 12 12 X 13 = 156
Do all square numbers have exactly 3 factors?
No. 81=9*9=3*27=1*81 81 has 5 factors and is a square number. 36=6*6=3*12=1*36=2*18=4*9 36 has 9 factors and is a square number. This doesn't mean that no square numbers have exactly 3 factors though, because: 9=3*3=1*9 9 has 3 factors and is a square number. 4=2*2=1*4 4 has 3 factors and is a square number. All square numbers have an odd number of factors though (because they have a whole number which multiplies by itself to get the number). Factors are whole numbers only, and not decimals. Hope this helps :)
What are three true statements about factors?
Numbers that can be multiplied together to get another number are its factors. A factor is a number that goes evenly into the number you're factoring. When you factor a number, say 12, you break it into its smallest parts. You could start with 6 x 2 and then 6 can be factored into 2 x 3, so the factors of 12 could be 2 x 2 x 3. To factor x^2 + 5x + 4 is to break it down into simpler parts.
What number is a multiple of 12 and a factor of 48?
12, 24, and 48 are all multiples of 12 and factors of 48.
Why does 12 go into 144?
Because it is a factor of that number. Factors are a fundamental part of number theory
