Question

How many four-digit numbers are there with less than 6 different prime factors?

Answer 1

Different prime factors of four digit numbers start at p1×p2×p3×p4×p5×p6 √p1×p2×p3×p4×p5×p6, actually. This boils down to mere counting possibilities, starting with 2×3×5×7×11×13=300302×3×5×7×11×13=30030. If this is a correct assumption, no such numbers will be found.

Answer 2

If we multiply least(or we can say first) 6 prime numbers i.e. 2, 3, 5, 7, 11 & 13, we get 2*3*5*7*11*13 = 30030 that means 30030 is the smallest number with 6 different prime factors. So, there can't be a 4 digit number which has 6 or more than 6 prime factors. We just have to find the number of 4 digit numbers i.e. 1000 to 9999 which are 9000 in number