What is the Greatest Common Factor of 78102 and 78120?

Greatest common factor (GCF) of 78102 and 78120 is 18.

GCF(78102,78120) = 18

We will now calculate the prime factors of 78102 and 78120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78102 and 78120.

How to find the GCF of 78102 and 78120?

We will first find the prime factorization of 78102 and 78120. After we will calculate the factors of 78102 and 78120 and find the biggest common factor number .

Step-1: Prime Factorization of 78102

Prime factors of 78102 are 2, 3, 4339. Prime factorization of 78102 in exponential form is:

78102 = 2¹ × 3² × 4339¹

Step-2: 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-3: Factors of 78102

List of positive integer factors of 78102 that divides 78102 without a remainder.

1, 2, 3, 6, 9, 18, 4339, 8678, 13017, 26034, 39051

Step-4: Factors of 78120

List of positive integer factors of 78120 that divides 78102 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78102 and 78120. The biggest common factor number is the GCF number.
So the greatest common factor 78102 and 78120 is 18.

Also check out the Least Common Multiple of 78102 and 78120