What is the Greatest Common Factor of 10705 and 10714?

Greatest common factor (GCF) of 10705 and 10714 is 1.

GCF(10705,10714) = 1

We will now calculate the prime factors of 10705 and 10714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10705 and 10714.

How to find the GCF of 10705 and 10714?

We will first find the prime factorization of 10705 and 10714. After we will calculate the factors of 10705 and 10714 and find the biggest common factor number .

Step-1: Prime Factorization of 10705

Prime factors of 10705 are 5, 2141. Prime factorization of 10705 in exponential form is:

10705 = 5¹ × 2141¹

Step-2: Prime Factorization of 10714

Prime factors of 10714 are 2, 11, 487. Prime factorization of 10714 in exponential form is:

10714 = 2¹ × 11¹ × 487¹

Step-3: Factors of 10705

List of positive integer factors of 10705 that divides 10705 without a remainder.

1, 5, 2141

Step-4: Factors of 10714

List of positive integer factors of 10714 that divides 10705 without a remainder.

1, 2, 11, 22, 487, 974, 5357

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10705 and 10714. The biggest common factor number is the GCF number.
So the greatest common factor 10705 and 10714 is 1.

Also check out the Least Common Multiple of 10705 and 10714