The number of divisors of $2^2.3^3.5^3.7^5$ of the form (4n+1).
Since $4n +1$ is odd the divisors must be of the form $3^a.5^b.7^c$
Since $a,b,c$ can have $4,4,6$ values respectively, answer should be $4.4.6$
This answer says that answer is 48 but this question came in my test in which the correct answer was 47.
Please explain without the use of modular arithmetic.