What is the Greatest Common Factor of 77259 and 77274?

Greatest common factor (GCF) of 77259 and 77274 is 3.

GCF(77259,77274) = 3

We will now calculate the prime factors of 77259 and 77274, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77259 and 77274.

How to find the GCF of 77259 and 77274?

We will first find the prime factorization of 77259 and 77274. After we will calculate the factors of 77259 and 77274 and find the biggest common factor number .

Step-1: Prime Factorization of 77259

Prime factors of 77259 are 3, 7, 13, 283. Prime factorization of 77259 in exponential form is:

77259 = 3¹ × 7¹ × 13¹ × 283¹

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 77259

List of positive integer factors of 77259 that divides 77259 without a remainder.

1, 3, 7, 13, 21, 39, 91, 273, 283, 849, 1981, 3679, 5943, 11037, 25753

Step-4: Factors of 77274

List of positive integer factors of 77274 that divides 77259 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 77259 and 77274. The biggest common factor number is the GCF number.
So the greatest common factor 77259 and 77274 is 3.

Also check out the Least Common Multiple of 77259 and 77274