What is the Greatest Common Factor of 10214 and 10218?

Greatest common factor (GCF) of 10214 and 10218 is 2.

GCF(10214,10218) = 2

We will now calculate the prime factors of 10214 and 10218, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10214 and 10218.

How to find the GCF of 10214 and 10218?

We will first find the prime factorization of 10214 and 10218. After we will calculate the factors of 10214 and 10218 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 10218

Prime factors of 10218 are 2, 3, 13, 131. Prime factorization of 10218 in exponential form is:

10218 = 2¹ × 3¹ × 13¹ × 131¹

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 10218

List of positive integer factors of 10218 that divides 10214 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 131, 262, 393, 786, 1703, 3406, 5109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10214 and 10218. The biggest common factor number is the GCF number.
So the greatest common factor 10214 and 10218 is 2.

Also check out the Least Common Multiple of 10214 and 10218