If 'N' is the minimum number which has 20 different positive integer factors, the value of 'N' is :
A) 240
B) 480
C) 1024
D) 15552
E) 2^21
A) 240
B) 480
C) 1024
D) 15552
E) 2^21
There's a nice rule that says:shankar.ashwin wrote:If 'N' is the minimum number which has 20 different positive integer factors, the value of 'N' is :
A) 240
B) 480
C) 1024
D) 15552
E) 2^21
If N = (p^a)(q^b)(r^c)... where p, q, r etc are prime numbers, then the total number of different positive divisors of N = (a+1)(b+1)(c+1)...
Now let's check the answer choices, beginning with the smallest (minimum) value.
240 = (2^4)(3^1)(5^1)
So, the number of different positive divisors of 240 = (4+1)(1+1)(1+1) = 20
So, the answer must be A
Cheers,
Brent
