What is the Greatest Common Factor of 78112 and 78120?

Greatest common factor (GCF) of 78112 and 78120 is 8.

GCF(78112,78120) = 8

We will now calculate the prime factors of 78112 and 78120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78112 and 78120.

How to find the GCF of 78112 and 78120?

We will first find the prime factorization of 78112 and 78120. After we will calculate the factors of 78112 and 78120 and find the biggest common factor number .

Step-1: Prime Factorization of 78112

Prime factors of 78112 are 2, 2441. Prime factorization of 78112 in exponential form is:

78112 = 2⁵ × 2441¹

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 78112

List of positive integer factors of 78112 that divides 78112 without a remainder.

1, 2, 4, 8, 16, 32, 2441, 4882, 9764, 19528, 39056

Step-4: Factors of 78120

List of positive integer factors of 78120 that divides 78112 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 78112 and 78120. The biggest common factor number is the GCF number.
So the greatest common factor 78112 and 78120 is 8.

Also check out the Least Common Multiple of 78112 and 78120