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The smallest number with exactly twelve divisors

numbersdivisorsprime-factors

The number 12 has six divisors: 1, 2, 3, 4, 6, 12.

What is the smallest positive whole number with exactly twelve divisors? Explain how the number of divisors can be read off the prime factorisation, and use that to search efficiently.

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If a number is 2 to the a times 3 to the b times 5 to the c ..., then its number of divisors is (a + 1)(b + 1)(c + 1)... Find the ways to write 12 as such a product and try the smallest primes.

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