What is the Greatest Common Factor of 2705 and 2714?

Greatest common factor (GCF) of 2705 and 2714 is 1.

GCF(2705,2714) = 1

We will now calculate the prime factors of 2705 and 2714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2705 and 2714.

How to find the GCF of 2705 and 2714?

We will first find the prime factorization of 2705 and 2714. After we will calculate the factors of 2705 and 2714 and find the biggest common factor number .

Step-1: Prime Factorization of 2705

Prime factors of 2705 are 5, 541. Prime factorization of 2705 in exponential form is:

2705 = 5¹ × 541¹

Step-2: Prime Factorization of 2714

Prime factors of 2714 are 2, 23, 59. Prime factorization of 2714 in exponential form is:

2714 = 2¹ × 23¹ × 59¹

Step-3: Factors of 2705

List of positive integer factors of 2705 that divides 2705 without a remainder.

1, 5, 541

Step-4: Factors of 2714

List of positive integer factors of 2714 that divides 2705 without a remainder.

1, 2, 23, 46, 59, 118, 1357

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2705 and 2714. The biggest common factor number is the GCF number.
So the greatest common factor 2705 and 2714 is 1.

Also check out the Least Common Multiple of 2705 and 2714