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# What is the least whole number with exactly 11 factors?

Updated: 9/17/2023

Wiki User

14y ago

210=1024, which has factors of 2i with i between 0 and 10 inclusive.

Explanation

If the prime factorization of a number is p1a*p2b*p3c...

the number of factors is (a+1)*(b+1)*(c+1)... [because each pi can be raised to the 0, 1, 2,..., up through the exponent, so there are a+1 choices for the exponent of p1, b+1 choices for the p2, etc.]. But because 11 is prime, there can only be one pi that will yield exactly 11 factors [if, for example, there were two prime factors of the number, you would need (a+1)*(b+1)=11 but because 11 is prime, this won't work unless one of a or b is zero] . 2 is the smallest Prime number, and 210=1024 is the smallest whole number with exactly 11 factors.

Wiki User

14y ago

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