Question

The number of divisors of $3630$, which have a remainder of $1$ when divided by $4$, is

• A. $12$
• B. $6$
• C. $4$
• D. $18$

Answer 1

The correct option is B $6$

The prime factorization of 3630:
$3630=2\times 3\times 5\times {11}^2$

we require divisors which have a remainder of 1 when divided by 4

$⟹$ odd divisors i.e., $1,3,5,11,{11}^2$

possible divisors are

$1$ $✓$

$1\times 3=3$

$1\times 5=5$ $✓$

$1\times 11=11$

$1\times 121=121$ $✓$

$3\times 5=15$

$3\times 11=33$ $✓$

$3\times 121=363$ $✓$

$5\times 11=55$

$5\times 121=605$ $✓$

all remaining odd divisors will repeat the above numbers as such only 6

numbers are divisors which divided by 4 leaves a remainder 1