What is the Greatest Common Factor of 31200 and 31206?

Greatest common factor (GCF) of 31200 and 31206 is 6.

GCF(31200,31206) = 6

We will now calculate the prime factors of 31200 and 31206, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31200 and 31206.

How to find the GCF of 31200 and 31206?

We will first find the prime factorization of 31200 and 31206. After we will calculate the factors of 31200 and 31206 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31206

Prime factors of 31206 are 2, 3, 7, 743. Prime factorization of 31206 in exponential form is:

31206 = 2¹ × 3¹ × 7¹ × 743¹

Step-3: Factors of 31200

List of positive integer factors of 31200 that divides 31200 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

Step-4: Factors of 31206

List of positive integer factors of 31206 that divides 31200 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 743, 1486, 2229, 4458, 5201, 10402, 15603

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31200 and 31206. The biggest common factor number is the GCF number.
So the greatest common factor 31200 and 31206 is 6.

Also check out the Least Common Multiple of 31200 and 31206