What is the Greatest Common Factor of 36120 and 36140?

Greatest common factor (GCF) of 36120 and 36140 is 20.

GCF(36120,36140) = 20

We will now calculate the prime factors of 36120 and 36140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36120 and 36140.

How to find the GCF of 36120 and 36140?

We will first find the prime factorization of 36120 and 36140. After we will calculate the factors of 36120 and 36140 and find the biggest common factor number .

Step-1: Prime Factorization of 36120

Prime factors of 36120 are 2, 3, 5, 7, 43. Prime factorization of 36120 in exponential form is:

36120 = 2³ × 3¹ × 5¹ × 7¹ × 43¹

Step-2: Prime Factorization of 36140

Prime factors of 36140 are 2, 5, 13, 139. Prime factorization of 36140 in exponential form is:

36140 = 2² × 5¹ × 13¹ × 139¹

Step-3: Factors of 36120

List of positive integer factors of 36120 that divides 36120 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 43, 56, 60, 70, 84, 86, 105, 120, 129, 140, 168, 172, 210, 215, 258, 280, 301, 344, 420, 430, 516, 602, 645, 840, 860, 903, 1032, 1204, 1290, 1505, 1720, 1806, 2408, 2580, 3010, 3612, 4515, 5160, 6020, 7224, 9030, 12040, 18060

Step-4: Factors of 36140

List of positive integer factors of 36140 that divides 36120 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 139, 260, 278, 556, 695, 1390, 1807, 2780, 3614, 7228, 9035, 18070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36120 and 36140. The biggest common factor number is the GCF number.
So the greatest common factor 36120 and 36140 is 20.

Also check out the Least Common Multiple of 36120 and 36140