What is the Greatest Common Factor of 10214 and 10234?

Greatest common factor (GCF) of 10214 and 10234 is 2.

GCF(10214,10234) = 2

We will now calculate the prime factors of 10214 and 10234, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10214 and 10234.

How to find the GCF of 10214 and 10234?

We will first find the prime factorization of 10214 and 10234. After we will calculate the factors of 10214 and 10234 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 10234

Prime factors of 10234 are 2, 7, 17, 43. Prime factorization of 10234 in exponential form is:

10234 = 2¹ × 7¹ × 17¹ × 43¹

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 10234

List of positive integer factors of 10234 that divides 10214 without a remainder.

1, 2, 7, 14, 17, 34, 43, 86, 119, 238, 301, 602, 731, 1462, 5117

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10214 and 10234. The biggest common factor number is the GCF number.
So the greatest common factor 10214 and 10234 is 2.

Also check out the Least Common Multiple of 10214 and 10234