What is the Greatest Common Factor of 31185 and 31200?

Greatest common factor (GCF) of 31185 and 31200 is 15.

GCF(31185,31200) = 15

We will now calculate the prime factors of 31185 and 31200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31185 and 31200.

How to find the GCF of 31185 and 31200?

We will first find the prime factorization of 31185 and 31200. After we will calculate the factors of 31185 and 31200 and find the biggest common factor number .

Step-1: Prime Factorization of 31185

Prime factors of 31185 are 3, 5, 7, 11. Prime factorization of 31185 in exponential form is:

31185 = 3⁴ × 5¹ × 7¹ × 11¹

Step-2: Prime Factorization of 31200

Prime factors of 31200 are 2, 3, 5, 13. Prime factorization of 31200 in exponential form is:

31200 = 2⁵ × 3¹ × 5² × 13¹

Step-3: Factors of 31185

List of positive integer factors of 31185 that divides 31185 without a remainder.

1, 3, 5, 7, 9, 11, 15, 21, 27, 33, 35, 45, 55, 63, 77, 81, 99, 105, 135, 165, 189, 231, 297, 315, 385, 405, 495, 567, 693, 891, 945, 1155, 1485, 2079, 2835, 3465, 4455, 6237, 10395

Step-4: Factors of 31200

List of positive integer factors of 31200 that divides 31185 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 39, 40, 48, 50, 52, 60, 65, 75, 78, 80, 96, 100, 104, 120, 130, 150, 156, 160, 195, 200, 208, 240, 260, 300, 312, 325, 390, 400, 416, 480, 520, 600, 624, 650, 780, 800, 975, 1040, 1200, 1248, 1300, 1560, 1950, 2080, 2400, 2600, 3120, 3900, 5200, 6240, 7800, 10400, 15600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31185 and 31200. The biggest common factor number is the GCF number.
So the greatest common factor 31185 and 31200 is 15.

Also check out the Least Common Multiple of 31185 and 31200