The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is\_\_\_\_
Answer: 150
Solutions · 1
Official solution
36=22×32. We need N divisible by 2 but not by 4 or 3 --- equivalently N=2m where gcd(m,18)=1.
Counting numbers with gcd(⋅,18)=1 in the appropriate range (translated via N=2m, 50≤m≤499 for 3-digit N), using the density of ϕ(18)/18=6/18=1/3 pattern per block of 18, gives:
\[\text{Total} = 150\]