What is the Greatest Common Factor of 39705 and 39714?

Greatest common factor (GCF) of 39705 and 39714 is 3.

GCF(39705,39714) = 3

We will now calculate the prime factors of 39705 and 39714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39705 and 39714.

How to find the GCF of 39705 and 39714?

We will first find the prime factorization of 39705 and 39714. After we will calculate the factors of 39705 and 39714 and find the biggest common factor number .

Step-1: Prime Factorization of 39705

Prime factors of 39705 are 3, 5, 2647. Prime factorization of 39705 in exponential form is:

39705 = 3¹ × 5¹ × 2647¹

Step-2: Prime Factorization of 39714

Prime factors of 39714 are 2, 3, 6619. Prime factorization of 39714 in exponential form is:

39714 = 2¹ × 3¹ × 6619¹

Step-3: Factors of 39705

List of positive integer factors of 39705 that divides 39705 without a remainder.

1, 3, 5, 15, 2647, 7941, 13235

Step-4: Factors of 39714

List of positive integer factors of 39714 that divides 39705 without a remainder.

1, 2, 3, 6, 6619, 13238, 19857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39705 and 39714. The biggest common factor number is the GCF number.
So the greatest common factor 39705 and 39714 is 3.

Also check out the Least Common Multiple of 39705 and 39714