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60. The number 60 has 12 divisors if you are counting the 1 and 60.

The divisors (given as factor pairs) are 1, 60, 2, 30, 3, 20, 4, 15, 5, 12, 6, 10.

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โˆ™ 2009-10-06 05:10:03
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Q: What is the smallest number with exactly twelve divisors?
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Related questions

What is the smallest number with 11 factors?

1024 has exactly eleven. 60 has twelve, so it has eleven as well.

How many divisors of twelve?

12 has six divisors.

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What is the smallest number with twelve factors?


What is the smallest number with exactly 12 factors?

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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There are infinitely many such numbers. For example, take any prime number to the 11th power and the result will have exactly twelve factors.

What is the smallest positive whole number that is divisibe with zero remainder by both twelve and ten?


List all abundant numbers 1 to 49?

An abundant number is any natural number (starting from 1) that is less than the sum of all its divisors excepting itself (the set of "all its divisors excepting itself" is also known as the set of its "proper divisors"). The lowest abundant number is twelve, and the first nine (all of those between one and fourty-nine, inclusive) are: 12 18 20 24 30 36 40 42 48

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How do you spell the number 12 in English?

The number 12 is spelled twelve.

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Well humans have exactly twelve pairs of ribs and that makes it 24.

What is the smallest prime factor of twelve is?

The smallest prime factor of 12 is 2.

Whats the smallest portable dryer commercially available?

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What is the smallest number with 12 factors?

(ITS 60. Factors: 1,2,3,4,5,6,10,12,15,20,30,60) The smallest positive integer with 12 divisors, including 1 and itself, is 60. They are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Notice that six of these divisors are smaller than the square-root of 60, and six of them are larger. (Only a number that is a perfect square can have an odd number of divisors, incidentally.)How can you find this result? To find quickly the number of divisors in any positive integer, first factorise it into prime factors, using exponents to count repetitions. Let's use 72 as an example: 72 = 8 X 9 = 2³ X 3². Thus, 3 occurs twice, and 2 occurs thrice. Every divisor of 72 contains 3 as a factor 0, 1, or 2 times; and it contains 2 as a factor either 0, 1, 2, or 3 times; and it can contain no other prime factor besides 2 and 3. Because there are 3 choices of how many times the divisor of 72 may contain 3 as a factor and 4 choices of how many times it may contain 4 as a factor, there are twelve possible divisors of 72. You can check this by asking how many divisors 72 has that are less than 9, the smallest positive integer whose square is greater than 72. It turns out that there are six, namely, 1, 2, 3, 4, 6, and 8. Its other six divisors must be at least 9, and they are found, by division, to be 9, 12, 18, 24, 36, and 72.Applying this logic, we now seek the smallest positive integer with twelve divisors: We can readily see that the number we seek will be a product of powers of the smallest primes. Moreover, it is plausible, even before multiplying it out, that it will be either the product of 2² X 3 X 5 or the product of 2³ X 3². And why is this? If we use 2² X 3 X 5, each of its divisors must present us 3 X 2 X 2 = 12 choices, as to the number of times each of its prime factors may be repeated in its prime factorization (obtained by adding 1 to each of the exponents and taking their product - noting that 1 is the exponent of 3 and 5, whilst 2 is the exponent we have shown for 2). Therefore, it will have 12 divisors. If we use 2³ X 3², each of its divisors must present us 4 X 3 = 12 choices, obtained by the same method.We can easily see that 2^11 (giving us 12 choices and, therefore, 12 divisors) is going to be much too large. On the other hand, four or more distinct prime factors (such as 2, 3, 5, and 7) will present us with with at least 2^4 choices and 2^4 = 16 divisors, which is more than we need. Now, since we can readily see that 2² X 3 X 5 = 60 is smaller than 2³ X 3² = 72, it is clear that 60 is the number we seek.

What is number twelve?

12, twelve, it's a number!

What continent has the smallest number of nations?

Excluding Antarctica, South America has the smallest number of nations. There are twelve independent countries on the continent of South America. Although French Guiana is physically located in South America, it is ruled by France as an overseas region and is considered to be part of that country.

How do you spell the number twelve?

The number 12 is "twelve" and the number 12th is "twelfth."

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Twelve over twelve as a mixed number can't appear as a mixed number like one and three fourths, so twelve over twelve equals a whole, or AKA, 1. There's your answer.

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48 has ten factors, 60 and 72 have twelve apiece, 80 is the next one with exactly ten.

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