What is the Greatest Common Factor of 34214 and 34220?

Greatest common factor (GCF) of 34214 and 34220 is 2.

GCF(34214,34220) = 2

We will now calculate the prime factors of 34214 and 34220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34214 and 34220.

How to find the GCF of 34214 and 34220?

We will first find the prime factorization of 34214 and 34220. After we will calculate the factors of 34214 and 34220 and find the biggest common factor number .

Step-1: Prime Factorization of 34214

Prime factors of 34214 are 2, 17107. Prime factorization of 34214 in exponential form is:

34214 = 2¹ × 17107¹

Step-2: Prime Factorization of 34220

Prime factors of 34220 are 2, 5, 29, 59. Prime factorization of 34220 in exponential form is:

34220 = 2² × 5¹ × 29¹ × 59¹

Step-3: Factors of 34214

List of positive integer factors of 34214 that divides 34214 without a remainder.

1, 2, 17107

Step-4: Factors of 34220

List of positive integer factors of 34220 that divides 34214 without a remainder.

1, 2, 4, 5, 10, 20, 29, 58, 59, 116, 118, 145, 236, 290, 295, 580, 590, 1180, 1711, 3422, 6844, 8555, 17110

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34214 and 34220. The biggest common factor number is the GCF number.
So the greatest common factor 34214 and 34220 is 2.

Also check out the Least Common Multiple of 34214 and 34220