What is the Greatest Common Factor of 705 and 714?

Greatest common factor (GCF) of 705 and 714 is 3.

GCF(705,714) = 3

We will now calculate the prime factors of 705 and 714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 705 and 714.

How to find the GCF of 705 and 714?

We will first find the prime factorization of 705 and 714. After we will calculate the factors of 705 and 714 and find the biggest common factor number .

Step-1: Prime Factorization of 705

Prime factors of 705 are 3, 5, 47. Prime factorization of 705 in exponential form is:

705 = 3¹ × 5¹ × 47¹

Step-2: 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-3: Factors of 705

List of positive integer factors of 705 that divides 705 without a remainder.

1, 3, 5, 15, 47, 141, 235

Step-4: Factors of 714

List of positive integer factors of 714 that divides 705 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 705 and 714. The biggest common factor number is the GCF number.
So the greatest common factor 705 and 714 is 3.

Also check out the Least Common Multiple of 705 and 714