What is the Greatest Common Factor of 714 and 731?

Greatest common factor (GCF) of 714 and 731 is 17.

GCF(714,731) = 17

We will now calculate the prime factors of 714 and 731, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 714 and 731.

How to find the GCF of 714 and 731?

We will first find the prime factorization of 714 and 731. After we will calculate the factors of 714 and 731 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 731

Prime factors of 731 are 17, 43. Prime factorization of 731 in exponential form is:

731 = 17¹ × 43¹

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 731

List of positive integer factors of 731 that divides 714 without a remainder.

1, 17, 43

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 714 and 731. The biggest common factor number is the GCF number.
So the greatest common factor 714 and 731 is 17.

Also check out the Least Common Multiple of 714 and 731