What is the Greatest Common Factor of 67114 and 67130?

Greatest common factor (GCF) of 67114 and 67130 is 2.

GCF(67114,67130) = 2

We will now calculate the prime factors of 67114 and 67130, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67114 and 67130.

How to find the GCF of 67114 and 67130?

We will first find the prime factorization of 67114 and 67130. After we will calculate the factors of 67114 and 67130 and find the biggest common factor number .

Step-1: Prime Factorization of 67114

Prime factors of 67114 are 2, 23, 1459. Prime factorization of 67114 in exponential form is:

67114 = 2¹ × 23¹ × 1459¹

Step-2: Prime Factorization of 67130

Prime factors of 67130 are 2, 5, 7, 137. Prime factorization of 67130 in exponential form is:

67130 = 2¹ × 5¹ × 7² × 137¹

Step-3: Factors of 67114

List of positive integer factors of 67114 that divides 67114 without a remainder.

1, 2, 23, 46, 1459, 2918, 33557

Step-4: Factors of 67130

List of positive integer factors of 67130 that divides 67114 without a remainder.

1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 137, 245, 274, 490, 685, 959, 1370, 1918, 4795, 6713, 9590, 13426, 33565

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67114 and 67130. The biggest common factor number is the GCF number.
So the greatest common factor 67114 and 67130 is 2.

Also check out the Least Common Multiple of 67114 and 67130