What is the Greatest Common Factor of 78120 and 78140?

Greatest common factor (GCF) of 78120 and 78140 is 20.

GCF(78120,78140) = 20

We will now calculate the prime factors of 78120 and 78140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78120 and 78140.

How to find the GCF of 78120 and 78140?

We will first find the prime factorization of 78120 and 78140. After we will calculate the factors of 78120 and 78140 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 78140

Prime factors of 78140 are 2, 5, 3907. Prime factorization of 78140 in exponential form is:

78140 = 2² × 5¹ × 3907¹

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 78140

List of positive integer factors of 78140 that divides 78120 without a remainder.

1, 2, 4, 5, 10, 20, 3907, 7814, 15628, 19535, 39070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78120 and 78140. The biggest common factor number is the GCF number.
So the greatest common factor 78120 and 78140 is 20.

Also check out the Least Common Multiple of 78120 and 78140