What is the Greatest Common Factor of 714 and 734?

Greatest common factor (GCF) of 714 and 734 is 2.

GCF(714,734) = 2

We will now calculate the prime factors of 714 and 734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 714 and 734.

How to find the GCF of 714 and 734?

We will first find the prime factorization of 714 and 734. After we will calculate the factors of 714 and 734 and find the biggest common factor number .

Step-1: Prime Factorization of 714

Prime factors of 714 are 2, 3, 7, 17. Prime factorization of 714 in exponential form is:

714 = 2¹ × 3¹ × 7¹ × 17¹

Step-2: Prime Factorization of 734

Prime factors of 734 are 2, 367. Prime factorization of 734 in exponential form is:

734 = 2¹ × 367¹

Step-3: Factors of 714

List of positive integer factors of 714 that divides 714 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357

Step-4: Factors of 734

List of positive integer factors of 734 that divides 714 without a remainder.

1, 2, 367

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 714 and 734. The biggest common factor number is the GCF number.
So the greatest common factor 714 and 734 is 2.

Also check out the Least Common Multiple of 714 and 734