What is the Greatest Common Factor of 67749 and 67764?

Greatest common factor (GCF) of 67749 and 67764 is 3.

GCF(67749,67764) = 3

We will now calculate the prime factors of 67749 and 67764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67749 and 67764.

How to find the GCF of 67749 and 67764?

We will first find the prime factorization of 67749 and 67764. After we will calculate the factors of 67749 and 67764 and find the biggest common factor number .

Step-1: Prime Factorization of 67749

Prime factors of 67749 are 3, 11, 2053. Prime factorization of 67749 in exponential form is:

67749 = 3¹ × 11¹ × 2053¹

Step-2: Prime Factorization of 67764

Prime factors of 67764 are 2, 3, 5647. Prime factorization of 67764 in exponential form is:

67764 = 2² × 3¹ × 5647¹

Step-3: Factors of 67749

List of positive integer factors of 67749 that divides 67749 without a remainder.

1, 3, 11, 33, 2053, 6159, 22583

Step-4: Factors of 67764

List of positive integer factors of 67764 that divides 67749 without a remainder.

1, 2, 3, 4, 6, 12, 5647, 11294, 16941, 22588, 33882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67749 and 67764. The biggest common factor number is the GCF number.
So the greatest common factor 67749 and 67764 is 3.

Also check out the Least Common Multiple of 67749 and 67764