What is the Greatest Common Factor of 13734 and 13749?

Greatest common factor (GCF) of 13734 and 13749 is 3.

GCF(13734,13749) = 3

We will now calculate the prime factors of 13734 and 13749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13734 and 13749.

How to find the GCF of 13734 and 13749?

We will first find the prime factorization of 13734 and 13749. After we will calculate the factors of 13734 and 13749 and find the biggest common factor number .

Step-1: Prime Factorization of 13734

Prime factors of 13734 are 2, 3, 7, 109. Prime factorization of 13734 in exponential form is:

13734 = 2¹ × 3² × 7¹ × 109¹

Step-2: Prime Factorization of 13749

Prime factors of 13749 are 3, 4583. Prime factorization of 13749 in exponential form is:

13749 = 3¹ × 4583¹

Step-3: Factors of 13734

List of positive integer factors of 13734 that divides 13734 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 109, 126, 218, 327, 654, 763, 981, 1526, 1962, 2289, 4578, 6867

Step-4: Factors of 13749

List of positive integer factors of 13749 that divides 13734 without a remainder.

1, 3, 4583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13734 and 13749. The biggest common factor number is the GCF number.
So the greatest common factor 13734 and 13749 is 3.

Also check out the Least Common Multiple of 13734 and 13749