What is the Greatest Common Factor of 77280 and 77288?

Greatest common factor (GCF) of 77280 and 77288 is 8.

GCF(77280,77288) = 8

We will now calculate the prime factors of 77280 and 77288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77280 and 77288.

How to find the GCF of 77280 and 77288?

We will first find the prime factorization of 77280 and 77288. After we will calculate the factors of 77280 and 77288 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 77288

Prime factors of 77288 are 2, 9661. Prime factorization of 77288 in exponential form is:

77288 = 2³ × 9661¹

Step-3: Factors of 77280

List of positive integer factors of 77280 that divides 77280 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

Step-4: Factors of 77288

List of positive integer factors of 77288 that divides 77280 without a remainder.

1, 2, 4, 8, 9661, 19322, 38644

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77280 and 77288. The biggest common factor number is the GCF number.
So the greatest common factor 77280 and 77288 is 8.

Also check out the Least Common Multiple of 77280 and 77288