30
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.
The answer is 48illustration:833 is a multiple of 49 which is more than 832the multiple which is immediately less than 833 is 784so the difference that must be subtracted is 832- 784 = 48
84
Translate this phrase into an algebraic equation The product of two consecutive multiple of three integers?
Any number less than 3.
It is 30.
30
It's a multiple of 5, a multiple of 6 (since it's between twin primes), and less than 50. The only possibility is 30. To check: The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30
The smallest number that has exactly three factors is 4.
24
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
The square of any prime number has exactly three factors: 22, 32, 52, etc.
4, 9, 25
105
27
98
49 has exactly 3 factors (1, 7, and 49) and is greater than 40 and less than 60.