What is the Greatest Common Factor of 77268 and 77274?

Greatest common factor (GCF) of 77268 and 77274 is 6.

GCF(77268,77274) = 6

We will now calculate the prime factors of 77268 and 77274, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77268 and 77274.

How to find the GCF of 77268 and 77274?

We will first find the prime factorization of 77268 and 77274. After we will calculate the factors of 77268 and 77274 and find the biggest common factor number .

Step-1: Prime Factorization of 77268

Prime factors of 77268 are 2, 3, 47, 137. Prime factorization of 77268 in exponential form is:

77268 = 2² × 3¹ × 47¹ × 137¹

Step-2: Prime Factorization of 77274

Prime factors of 77274 are 2, 3, 53. Prime factorization of 77274 in exponential form is:

77274 = 2¹ × 3⁶ × 53¹

Step-3: Factors of 77268

List of positive integer factors of 77268 that divides 77268 without a remainder.

1, 2, 3, 4, 6, 12, 47, 94, 137, 141, 188, 274, 282, 411, 548, 564, 822, 1644, 6439, 12878, 19317, 25756, 38634

Step-4: Factors of 77274

List of positive integer factors of 77274 that divides 77268 without a remainder.

1, 2, 3, 6, 9, 18, 27, 53, 54, 81, 106, 159, 162, 243, 318, 477, 486, 729, 954, 1431, 1458, 2862, 4293, 8586, 12879, 25758, 38637

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77268 and 77274. The biggest common factor number is the GCF number.
So the greatest common factor 77268 and 77274 is 6.

Also check out the Least Common Multiple of 77268 and 77274