What is the Greatest Common Factor of 3735 and 3749?

Greatest common factor (GCF) of 3735 and 3749 is 1.

GCF(3735,3749) = 1

We will now calculate the prime factors of 3735 and 3749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3735 and 3749.

How to find the GCF of 3735 and 3749?

We will first find the prime factorization of 3735 and 3749. After we will calculate the factors of 3735 and 3749 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 3749

Prime factors of 3749 are 23, 163. Prime factorization of 3749 in exponential form is:

3749 = 23¹ × 163¹

Step-3: Factors of 3735

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

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

Step-4: Factors of 3749

List of positive integer factors of 3749 that divides 3735 without a remainder.

1, 23, 163

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3735 and 3749. The biggest common factor number is the GCF number.
So the greatest common factor 3735 and 3749 is 1.

Also check out the Least Common Multiple of 3735 and 3749