How many factors of 2⁷ × 3³ × 5⁴ × 7 are even numbers?
280
280 is correct.
A factor is even only if it contains at least one 2. So the power of 2 can be chosen from 1 to 7 (7 ways), the power of 3 from 0 to 3 (4 ways), the power of 5 from 0 to 4 (5 ways) and the power of 7 from 0 to 1 (2 ways).
Even factors = \(7 \times 4 \times 5 \times 2 = 280\)
Check: total factors = \(8 \times 4 \times 5 \times 2 = 320\) and odd factors = \(4 \times 5 \times 2 = 40\), and \(320 - 40 = 280\).
Find the median of all positive factors of 48.
Which of the following numbers is divisible by 12?