Question

If n = 2^10 * 3^14* 5^8, how many of the natural-number factors of n are multiples of 150?

Answer 1

\[150 = 6*25 = 2*3*5^2\]

that means :
the exponent on \(2\) can be between \(1\) and \(10\) = \(10\) ways
the exponent on \(3\) can be between \(1\) and \(14\) = \(14\) ways
the exponent on \(5\) can be between \(2\) and \(8\) = \(7\) ways

then total number of factors that are multiples of \(150\) would be : \(10\times 14\times 7\)