maths poser

[columbus]

Just back from British Super Bikes at Croft and someone set a poser and despite much brain searching left without the Answer. Does anyone please know of a number that has exactly 15 factors all help appreciated, before I go insane. Thanks a lot in anticipation

[factor-fiction]

A multiple of the first 13 prime numbers:
2, 3, 5, 7, 11,13,17, 19, etc
I don't have acalculator with me

[Fibonacci]

As it has an odd number of factors it muts be a square number

144 seems to fit the bill
- 1,144,2,72,3,48,4,36,6,24,8,18,9,16,12

[factor-fiction]

Should say first 15 prime numbers.
2 x 3 x 7x 11x13 x ....x 61

The answer is a very big number! ( a little under 2 millon milllion million I estimate)
This answer assumes you are not counting 1 as a factor, and that all 15 factors must be unique x 61

[factor-fiction]

Fibonnaci's answer is much better than mine! (Although mine is correct also I think, and yes it's a square number too).

[columbus]

thanks a lot finobacci 144 seems to fit the bill, to factor30, I am sure ! is included but thanks to you both for your help.

[crofter]

144 works because it can be expressed as a product of factors in the form 1x2x2x2x2x3x3 =16x9=144.

1 is always considered to be a factor in these situations , but is not considered a PRIME factor. 2 and 3 are prime factors of 144.

Another solution will be 1x2x2x3x3x3x3 = 4x81 =324 for the same reasons. Another is 1x7x7x7x7x11x11 and it becomes clear that there is a countably infinite number of solutions that can be formed from ANY TWO prime numbers.

144 is unique in that it is the smallest natural number to have the property to which you refer.