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.
Add 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
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.
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 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
What is the smallest number with exactly 6 factors?
12
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 is the smallest positive integer that has exactly 6 factors?
The smallest positive integer that has exactly 6 factors is 12. To determine the number of factors an integer has, we can use its prime factorization. In the case of 12, its prime factorization is 2^2 * 3, which means it has (2+1)(1+1) = 6 factors.
What is the smallest number that can be divided exactly by 6 and 12?
12.
What is the smallest number that has six factors?
12
What is the smallest number that has 12 25 and 30 as factors?
The smallest number that has 9 and 12 as factors is 36.
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 exactly nine factors?
36. (Factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36.)
What is the smallest number with 6 factors?
12 is as it has 6 factors and is the smallest and first to have. Factors of 12= 1, 2, 3, 4, 6, and 12
What is the smallest number that can be divided exactly by 3 and 4?
12
What is the smallest whole number that has exactly 6 distinct positive divisors?
12
What is the smallest number that has 12 30 and 36 as factors?
180
