What is the Greatest Common Factor of 28200 and 28214?

Greatest common factor (GCF) of 28200 and 28214 is 2.

GCF(28200,28214) = 2

We will now calculate the prime factors of 28200 and 28214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28200 and 28214.

How to find the GCF of 28200 and 28214?

We will first find the prime factorization of 28200 and 28214. After we will calculate the factors of 28200 and 28214 and find the biggest common factor number .

Step-1: Prime Factorization of 28200

Prime factors of 28200 are 2, 3, 5, 47. Prime factorization of 28200 in exponential form is:

28200 = 2³ × 3¹ × 5² × 47¹

Step-2: Prime Factorization of 28214

Prime factors of 28214 are 2, 14107. Prime factorization of 28214 in exponential form is:

28214 = 2¹ × 14107¹

Step-3: Factors of 28200

List of positive integer factors of 28200 that divides 28200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 47, 50, 60, 75, 94, 100, 120, 141, 150, 188, 200, 235, 282, 300, 376, 470, 564, 600, 705, 940, 1128, 1175, 1410, 1880, 2350, 2820, 3525, 4700, 5640, 7050, 9400, 14100

Step-4: Factors of 28214

List of positive integer factors of 28214 that divides 28200 without a remainder.

1, 2, 14107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28200 and 28214. The biggest common factor number is the GCF number.
So the greatest common factor 28200 and 28214 is 2.

Also check out the Least Common Multiple of 28200 and 28214