What is the Greatest Common Factor of 67758 and 67774?

Greatest common factor (GCF) of 67758 and 67774 is 2.

GCF(67758,67774) = 2

We will now calculate the prime factors of 67758 and 67774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67758 and 67774.

How to find the GCF of 67758 and 67774?

We will first find the prime factorization of 67758 and 67774. After we will calculate the factors of 67758 and 67774 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 67774

Prime factors of 67774 are 2, 7, 47, 103. Prime factorization of 67774 in exponential form is:

67774 = 2¹ × 7¹ × 47¹ × 103¹

Step-3: Factors of 67758

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

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

Step-4: Factors of 67774

List of positive integer factors of 67774 that divides 67758 without a remainder.

1, 2, 7, 14, 47, 94, 103, 206, 329, 658, 721, 1442, 4841, 9682, 33887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67758 and 67774. The biggest common factor number is the GCF number.
So the greatest common factor 67758 and 67774 is 2.

Also check out the Least Common Multiple of 67758 and 67774