What is the Greatest Common Factor of 36100 and 36120?

Greatest common factor (GCF) of 36100 and 36120 is 20.

GCF(36100,36120) = 20

We will now calculate the prime factors of 36100 and 36120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36100 and 36120.

How to find the GCF of 36100 and 36120?

We will first find the prime factorization of 36100 and 36120. After we will calculate the factors of 36100 and 36120 and find the biggest common factor number .

Step-1: Prime Factorization of 36100

Prime factors of 36100 are 2, 5, 19. Prime factorization of 36100 in exponential form is:

36100 = 2² × 5² × 19²

Step-2: 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-3: Factors of 36100

List of positive integer factors of 36100 that divides 36100 without a remainder.

1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 190, 361, 380, 475, 722, 950, 1444, 1805, 1900, 3610, 7220, 9025, 18050

Step-4: Factors of 36120

List of positive integer factors of 36120 that divides 36100 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36100 and 36120. The biggest common factor number is the GCF number.
So the greatest common factor 36100 and 36120 is 20.

Also check out the Least Common Multiple of 36100 and 36120