What is the Greatest Common Factor of 31186 and 31200?

Greatest common factor (GCF) of 31186 and 31200 is 2.

GCF(31186,31200) = 2

We will now calculate the prime factors of 31186 and 31200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31186 and 31200.

How to find the GCF of 31186 and 31200?

We will first find the prime factorization of 31186 and 31200. After we will calculate the factors of 31186 and 31200 and find the biggest common factor number .

Step-1: Prime Factorization of 31186

Prime factors of 31186 are 2, 31, 503. Prime factorization of 31186 in exponential form is:

31186 = 2¹ × 31¹ × 503¹

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 31186

List of positive integer factors of 31186 that divides 31186 without a remainder.

1, 2, 31, 62, 503, 1006, 15593

Step-4: Factors of 31200

List of positive integer factors of 31200 that divides 31186 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 31186 and 31200. The biggest common factor number is the GCF number.
So the greatest common factor 31186 and 31200 is 2.

Also check out the Least Common Multiple of 31186 and 31200