What is the Greatest Common Factor of 77350 and 77364?

Greatest common factor (GCF) of 77350 and 77364 is 14.

GCF(77350,77364) = 14

We will now calculate the prime factors of 77350 and 77364, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77350 and 77364.

How to find the GCF of 77350 and 77364?

We will first find the prime factorization of 77350 and 77364. After we will calculate the factors of 77350 and 77364 and find the biggest common factor number .

Step-1: Prime Factorization of 77350

Prime factors of 77350 are 2, 5, 7, 13, 17. Prime factorization of 77350 in exponential form is:

77350 = 2¹ × 5² × 7¹ × 13¹ × 17¹

Step-2: Prime Factorization of 77364

Prime factors of 77364 are 2, 3, 7, 307. Prime factorization of 77364 in exponential form is:

77364 = 2² × 3² × 7¹ × 307¹

Step-3: Factors of 77350

List of positive integer factors of 77350 that divides 77350 without a remainder.

1, 2, 5, 7, 10, 13, 14, 17, 25, 26, 34, 35, 50, 65, 70, 85, 91, 119, 130, 170, 175, 182, 221, 238, 325, 350, 425, 442, 455, 595, 650, 850, 910, 1105, 1190, 1547, 2210, 2275, 2975, 3094, 4550, 5525, 5950, 7735, 11050, 15470, 38675

Step-4: Factors of 77364

List of positive integer factors of 77364 that divides 77350 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252, 307, 614, 921, 1228, 1842, 2149, 2763, 3684, 4298, 5526, 6447, 8596, 11052, 12894, 19341, 25788, 38682

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77350 and 77364. The biggest common factor number is the GCF number.
So the greatest common factor 77350 and 77364 is 14.

Also check out the Least Common Multiple of 77350 and 77364