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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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I BELIEVE IT IS 156 THE SMALLEST NUMBER 4 AND 6 GO INTO IS 12 12 X 13 = 156
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What are three true statements about factors?
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What number is a multiple of 12 and a factor of 48?
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Because it is a factor of that number. Factors are a fundamental part of number theory
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12
What is the least positive integer that has exactly 13 factors?
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12.
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12
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What is the smallest number with nineteen factors?
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12
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