Find the number of divisors of 3630

What we need is a divisor of the form 4n+1, a clear odd number,
So removing the even factor(s), the number becomes, 363*5
5 being one such number!
Clearly neither 363, nor 3 are such numbers
So the number we have now is, 121, which is one such number
but its factor(s) 11 does not come in this category,
while 11*3= 33 is 4*8+1,
Though 11*5=55 is not involved, 121*5=604+1 is included
1 being a factor takes our count to 5

Can someone help me find the lost number[7][7]

Thank you
:-)