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

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

Grade:12

3 Answers

Ravleen Kaur
askIITians Faculty 1452 Points
6 years ago
Hello Student,
The prime factorization of 3630 = 2x3x5x112
now, a divisor will be of the form (4n+1), if thye diviswor is formed with the help of a number of type (4n+1) taken any number of times
OR
(4n+3) taken even number of times.
Hence, the requitred divisors are
1, 5, 3X11, 112, 5x112, 5x3X11
Total number of possible divisors =6
Regards,
IHE
SRINIVAS
10 Points
6 years ago
Wrong sir............ Also like 165 too....... And 605 too will be....... Though answer is wrong.............
Ravleen Kaur
askIITians Faculty 1452 Points
6 years ago
Hello Student,

The answer left incomplete last time due to some system issue. Kindly go through this.

The prime factorization of 3630 = 2x3x5x112
now, a divisor will be of the form (4n+1), if thye diviswor is formed with the help of a number of type (4n+1) taken any number of times
OR
(4n+3) taken even number of times.
Hence, the requitred divisors are
1, 5, 3X11, 112, 5x112, 5x3X11
Total number of possible divisors =6
Regards,
IHE

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