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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.
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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
