What is the Greatest Common Factor of 31200 and 31213?

Greatest common factor (GCF) of 31200 and 31213 is 13.

GCF(31200,31213) = 13

We will now calculate the prime factors of 31200 and 31213, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31200 and 31213.

How to find the GCF of 31200 and 31213?

We will first find the prime factorization of 31200 and 31213. After we will calculate the factors of 31200 and 31213 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 31213

Prime factors of 31213 are 7, 13. Prime factorization of 31213 in exponential form is:

31213 = 7⁴ × 13¹

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 31213

List of positive integer factors of 31213 that divides 31200 without a remainder.

1, 7, 13, 49, 91, 343, 637, 2401, 4459

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31200 and 31213. The biggest common factor number is the GCF number.
So the greatest common factor 31200 and 31213 is 13.

Also check out the Least Common Multiple of 31200 and 31213