What is the Greatest Common Factor of 77268 and 77280?

Greatest common factor (GCF) of 77268 and 77280 is 12.

GCF(77268,77280) = 12

We will now calculate the prime factors of 77268 and 77280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77268 and 77280.

How to find the GCF of 77268 and 77280?

We will first find the prime factorization of 77268 and 77280. After we will calculate the factors of 77268 and 77280 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 77280

Prime factors of 77280 are 2, 3, 5, 7, 23. Prime factorization of 77280 in exponential form is:

77280 = 2⁵ × 3¹ × 5¹ × 7¹ × 23¹

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 77280

List of positive integer factors of 77280 that divides 77268 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 23, 24, 28, 30, 32, 35, 40, 42, 46, 48, 56, 60, 69, 70, 80, 84, 92, 96, 105, 112, 115, 120, 138, 140, 160, 161, 168, 184, 210, 224, 230, 240, 276, 280, 322, 336, 345, 368, 420, 460, 480, 483, 552, 560, 644, 672, 690, 736, 805, 840, 920, 966, 1104, 1120, 1288, 1380, 1610, 1680, 1840, 1932, 2208, 2415, 2576, 2760, 3220, 3360, 3680, 3864, 4830, 5152, 5520, 6440, 7728, 9660, 11040, 12880, 15456, 19320, 25760, 38640

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77268 and 77280. The biggest common factor number is the GCF number.
So the greatest common factor 77268 and 77280 is 12.

Also check out the Least Common Multiple of 77268 and 77280