What is the Greatest Common Factor of 854 and 868?

Greatest common factor (GCF) of 854 and 868 is 14.

GCF(854,868) = 14

We will now calculate the prime factors of 854 and 868, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 854 and 868.

How to find the GCF of 854 and 868?

We will first find the prime factorization of 854 and 868. After we will calculate the factors of 854 and 868 and find the biggest common factor number .

Step-1: Prime Factorization of 854

Prime factors of 854 are 2, 7, 61. Prime factorization of 854 in exponential form is:

854 = 2¹ × 7¹ × 61¹

Step-2: Prime Factorization of 868

Prime factors of 868 are 2, 7, 31. Prime factorization of 868 in exponential form is:

868 = 2² × 7¹ × 31¹

Step-3: Factors of 854

List of positive integer factors of 854 that divides 854 without a remainder.

1, 2, 7, 14, 61, 122, 427

Step-4: Factors of 868

List of positive integer factors of 868 that divides 854 without a remainder.

1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 854 and 868. The biggest common factor number is the GCF number.
So the greatest common factor 854 and 868 is 14.

Also check out the Least Common Multiple of 854 and 868