What is the Greatest Common Factor of 67774 and 67782?

Greatest common factor (GCF) of 67774 and 67782 is 2.

GCF(67774,67782) = 2

We will now calculate the prime factors of 67774 and 67782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67774 and 67782.

How to find the GCF of 67774 and 67782?

We will first find the prime factorization of 67774 and 67782. After we will calculate the factors of 67774 and 67782 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 67782

Prime factors of 67782 are 2, 3, 11, 13, 79. Prime factorization of 67782 in exponential form is:

67782 = 2¹ × 3¹ × 11¹ × 13¹ × 79¹

Step-3: Factors of 67774

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

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

Step-4: Factors of 67782

List of positive integer factors of 67782 that divides 67774 without a remainder.

1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 79, 143, 158, 237, 286, 429, 474, 858, 869, 1027, 1738, 2054, 2607, 3081, 5214, 6162, 11297, 22594, 33891

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67774 and 67782. The biggest common factor number is the GCF number.
So the greatest common factor 67774 and 67782 is 2.

Also check out the Least Common Multiple of 67774 and 67782