What is the Greatest Common Factor of 31200 and 31216?

Greatest common factor (GCF) of 31200 and 31216 is 16.

GCF(31200,31216) = 16

We will now calculate the prime factors of 31200 and 31216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31200 and 31216.

How to find the GCF of 31200 and 31216?

We will first find the prime factorization of 31200 and 31216. After we will calculate the factors of 31200 and 31216 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 31216

Prime factors of 31216 are 2, 1951. Prime factorization of 31216 in exponential form is:

31216 = 2⁴ × 1951¹

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 31216

List of positive integer factors of 31216 that divides 31200 without a remainder.

1, 2, 4, 8, 16, 1951, 3902, 7804, 15608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31200 and 31216. The biggest common factor number is the GCF number.
So the greatest common factor 31200 and 31216 is 16.

Also check out the Least Common Multiple of 31200 and 31216