What is the Greatest Common Factor of 77280 and 77295?

Greatest common factor (GCF) of 77280 and 77295 is 15.

GCF(77280,77295) = 15

We will now calculate the prime factors of 77280 and 77295, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77280 and 77295.

How to find the GCF of 77280 and 77295?

We will first find the prime factorization of 77280 and 77295. After we will calculate the factors of 77280 and 77295 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 77295

Prime factors of 77295 are 3, 5, 5153. Prime factorization of 77295 in exponential form is:

77295 = 3¹ × 5¹ × 5153¹

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 77295

List of positive integer factors of 77295 that divides 77280 without a remainder.

1, 3, 5, 15, 5153, 15459, 25765

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77280 and 77295. The biggest common factor number is the GCF number.
So the greatest common factor 77280 and 77295 is 15.

Also check out the Least Common Multiple of 77280 and 77295