What is the Greatest Common Factor of 610 and 614?

Greatest common factor (GCF) of 610 and 614 is 2.

GCF(610,614) = 2

We will now calculate the prime factors of 610 and 614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 610 and 614.

How to find the GCF of 610 and 614?

We will first find the prime factorization of 610 and 614. After we will calculate the factors of 610 and 614 and find the biggest common factor number .

Step-1: Prime Factorization of 610

Prime factors of 610 are 2, 5, 61. Prime factorization of 610 in exponential form is:

610 = 2¹ × 5¹ × 61¹

Step-2: Prime Factorization of 614

Prime factors of 614 are 2, 307. Prime factorization of 614 in exponential form is:

614 = 2¹ × 307¹

Step-3: Factors of 610

List of positive integer factors of 610 that divides 610 without a remainder.

1, 2, 5, 10, 61, 122, 305

Step-4: Factors of 614

List of positive integer factors of 614 that divides 610 without a remainder.

1, 2, 307

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 610 and 614. The biggest common factor number is the GCF number.
So the greatest common factor 610 and 614 is 2.

Also check out the Least Common Multiple of 610 and 614