Problem
NT-B1-M01-P012 Even Divisors
#12
★★☆☆☆ Level 2 of 5
How many positive even divisors does \(2^5\cdot3^2\cdot5\) have?
In an even divisor, the exponent of \(2\) is not zero.
The exponent of \(2\) can be \(1,2,3,4,5\): \(5\) choices. The exponent of \(3\) has \(3\) choices: \(0,1,2\). The exponent of \(5\) has \(2\) choices: \(0,1\). Hence there are \(5\cdot3\cdot2=30\) even divisors.
Checks that the parity condition changes the range of one exponent.