What is the Greatest Common Factor of 3723 and 3735?

Greatest common factor (GCF) of 3723 and 3735 is 3.

GCF(3723,3735) = 3

We will now calculate the prime factors of 3723 and 3735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3723 and 3735.

How to find the GCF of 3723 and 3735?

We will first find the prime factorization of 3723 and 3735. After we will calculate the factors of 3723 and 3735 and find the biggest common factor number .

Step-1: Prime Factorization of 3723

Prime factors of 3723 are 3, 17, 73. Prime factorization of 3723 in exponential form is:

3723 = 3¹ × 17¹ × 73¹

Step-2: Prime Factorization of 3735

Prime factors of 3735 are 3, 5, 83. Prime factorization of 3735 in exponential form is:

3735 = 3² × 5¹ × 83¹

Step-3: Factors of 3723

List of positive integer factors of 3723 that divides 3723 without a remainder.

1, 3, 17, 51, 73, 219, 1241

Step-4: Factors of 3735

List of positive integer factors of 3735 that divides 3723 without a remainder.

1, 3, 5, 9, 15, 45, 83, 249, 415, 747, 1245

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3723 and 3735. The biggest common factor number is the GCF number.
So the greatest common factor 3723 and 3735 is 3.

Also check out the Least Common Multiple of 3723 and 3735