What is the Greatest Common Factor of 67749 and 67758?

Greatest common factor (GCF) of 67749 and 67758 is 3.

GCF(67749,67758) = 3

We will now calculate the prime factors of 67749 and 67758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67749 and 67758.

How to find the GCF of 67749 and 67758?

We will first find the prime factorization of 67749 and 67758. After we will calculate the factors of 67749 and 67758 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 67758

Prime factors of 67758 are 2, 3, 23, 491. Prime factorization of 67758 in exponential form is:

67758 = 2¹ × 3¹ × 23¹ × 491¹

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 67758

List of positive integer factors of 67758 that divides 67749 without a remainder.

1, 2, 3, 6, 23, 46, 69, 138, 491, 982, 1473, 2946, 11293, 22586, 33879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67749 and 67758. The biggest common factor number is the GCF number.
So the greatest common factor 67749 and 67758 is 3.

Also check out the Least Common Multiple of 67749 and 67758