What is the Greatest Common Factor of 78120 and 78134?

Greatest common factor (GCF) of 78120 and 78134 is 14.

GCF(78120,78134) = 14

We will now calculate the prime factors of 78120 and 78134, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78120 and 78134.

How to find the GCF of 78120 and 78134?

We will first find the prime factorization of 78120 and 78134. After we will calculate the factors of 78120 and 78134 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 78134

Prime factors of 78134 are 2, 7, 5581. Prime factorization of 78134 in exponential form is:

78134 = 2¹ × 7¹ × 5581¹

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 78134

List of positive integer factors of 78134 that divides 78120 without a remainder.

1, 2, 7, 14, 5581, 11162, 39067

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78120 and 78134. The biggest common factor number is the GCF number.
So the greatest common factor 78120 and 78134 is 14.

Also check out the Least Common Multiple of 78120 and 78134