What is the Greatest Common Factor of 31200 and 31204?

Greatest common factor (GCF) of 31200 and 31204 is 4.

GCF(31200,31204) = 4

We will now calculate the prime factors of 31200 and 31204, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31200 and 31204.

How to find the GCF of 31200 and 31204?

We will first find the prime factorization of 31200 and 31204. After we will calculate the factors of 31200 and 31204 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 31204

Prime factors of 31204 are 2, 29, 269. Prime factorization of 31204 in exponential form is:

31204 = 2² × 29¹ × 269¹

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 31204

List of positive integer factors of 31204 that divides 31200 without a remainder.

1, 2, 4, 29, 58, 116, 269, 538, 1076, 7801, 15602

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31200 and 31204. The biggest common factor number is the GCF number.
So the greatest common factor 31200 and 31204 is 4.

Also check out the Least Common Multiple of 31200 and 31204