What is the Greatest Common Factor of 10214 and 10222?

Greatest common factor (GCF) of 10214 and 10222 is 2.

GCF(10214,10222) = 2

We will now calculate the prime factors of 10214 and 10222, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10214 and 10222.

How to find the GCF of 10214 and 10222?

We will first find the prime factorization of 10214 and 10222. After we will calculate the factors of 10214 and 10222 and find the biggest common factor number .

Step-1: Prime Factorization of 10214

Prime factors of 10214 are 2, 5107. Prime factorization of 10214 in exponential form is:

10214 = 2¹ × 5107¹

Step-2: Prime Factorization of 10222

Prime factors of 10222 are 2, 19, 269. Prime factorization of 10222 in exponential form is:

10222 = 2¹ × 19¹ × 269¹

Step-3: Factors of 10214

List of positive integer factors of 10214 that divides 10214 without a remainder.

1, 2, 5107

Step-4: Factors of 10222

List of positive integer factors of 10222 that divides 10214 without a remainder.

1, 2, 19, 38, 269, 538, 5111

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10214 and 10222. The biggest common factor number is the GCF number.
So the greatest common factor 10214 and 10222 is 2.

Also check out the Least Common Multiple of 10214 and 10222