Question

What is the smallest number that has exactly 12 factors?

Answer 1

12!

Answer 2

like factorial of 12, not 12

Answer 3

Is it:

\[2^{12}\]

Answer 4

nop..i'll tell the ans later,,but thats not the ans..

Answer 5

Isnt it 60?

Answer 6

yep..60..

Answer 7

Boosh.

Answer 8

but i'd like to know the method..

Answer 9

2.5.3.4.5.6.10.12.15.20.30.60 so this is what you meant :C, numbers of factors.

not them multiplying each other or different factors ._.

Answer 10

ofcorse thats what i meant,,question was quite clear,.anyways,,anyone can show some method to do it?

Answer 11

by the way you repeated 5 and missed 1 !! :P

Answer 12

different factors?

Answer 13

yes..2.5.3.4.1.6.10.12.15.20.30.60
these are the 12 factors..
i want the method of knowing how 60 was smallest no. with exact 12 factors..

Answer 14

tests and trials!

Answer 15

well..i have 1 method,,i want to see if any one else posts any..

Answer 16

so u mean 12 divisors not factors

Answer 17

well isnt 4 a factor of 8 ?

Answer 18

or is it the other way around? 8 a factor of 4 ?

Answer 19

let me think

Answer 20

are u familiar with prime factorization and divisors of a positive integer?

Answer 21

yes..

Answer 22

12=3*2*2
three smallest factors of 12 are 2,2 and 3
3*2*2=(2+1)(1+1)(1+1)
u just need to choose three different prime numbers with exponents 1,1,2 to make the number
largest exponent for smallest prime number
i choose 2 for 2
1 for 3 and 1 for 5
so
n=2^2*3*5=60

Answer 23

excellent !! :)