What is the Greatest Common Factor of 77270 and 77280?

Greatest common factor (GCF) of 77270 and 77280 is 10.

GCF(77270,77280) = 10

We will now calculate the prime factors of 77270 and 77280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77270 and 77280.

How to find the GCF of 77270 and 77280?

We will first find the prime factorization of 77270 and 77280. After we will calculate the factors of 77270 and 77280 and find the biggest common factor number .

Step-1: Prime Factorization of 77270

Prime factors of 77270 are 2, 5, 7727. Prime factorization of 77270 in exponential form is:

77270 = 2¹ × 5¹ × 7727¹

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 77270

List of positive integer factors of 77270 that divides 77270 without a remainder.

1, 2, 5, 10, 7727, 15454, 38635

Step-4: Factors of 77280

List of positive integer factors of 77280 that divides 77270 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 77270 and 77280. The biggest common factor number is the GCF number.
So the greatest common factor 77270 and 77280 is 10.

Also check out the Least Common Multiple of 77270 and 77280