What is the Greatest Common Factor of 78120 and 78138?

Greatest common factor (GCF) of 78120 and 78138 is 18.

GCF(78120,78138) = 18

We will now calculate the prime factors of 78120 and 78138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78120 and 78138.

How to find the GCF of 78120 and 78138?

We will first find the prime factorization of 78120 and 78138. After we will calculate the factors of 78120 and 78138 and find the biggest common factor number .

Step-1: Prime Factorization of 78120

Prime factors of 78120 are 2, 3, 5, 7, 31. Prime factorization of 78120 in exponential form is:

78120 = 2³ × 3² × 5¹ × 7¹ × 31¹

Step-2: Prime Factorization of 78138

Prime factors of 78138 are 2, 3, 1447. Prime factorization of 78138 in exponential form is:

78138 = 2¹ × 3³ × 1447¹

Step-3: Factors of 78120

List of positive integer factors of 78120 that divides 78120 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 31, 35, 36, 40, 42, 45, 56, 60, 62, 63, 70, 72, 84, 90, 93, 105, 120, 124, 126, 140, 155, 168, 180, 186, 210, 217, 248, 252, 279, 280, 310, 315, 360, 372, 420, 434, 465, 504, 558, 620, 630, 651, 744, 840, 868, 930, 1085, 1116, 1240, 1260, 1302, 1395, 1736, 1860, 1953, 2170, 2232, 2520, 2604, 2790, 3255, 3720, 3906, 4340, 5208, 5580, 6510, 7812, 8680, 9765, 11160, 13020, 15624, 19530, 26040, 39060

Step-4: Factors of 78138

List of positive integer factors of 78138 that divides 78120 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 1447, 2894, 4341, 8682, 13023, 26046, 39069

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78120 and 78138. The biggest common factor number is the GCF number.
So the greatest common factor 78120 and 78138 is 18.

Also check out the Least Common Multiple of 78120 and 78138