What is the Greatest Common Factor of 854 and 864?

Greatest common factor (GCF) of 854 and 864 is 2.

GCF(854,864) = 2

We will now calculate the prime factors of 854 and 864, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 854 and 864.

How to find the GCF of 854 and 864?

We will first find the prime factorization of 854 and 864. After we will calculate the factors of 854 and 864 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 864

Prime factors of 864 are 2, 3. Prime factorization of 864 in exponential form is:

864 = 2⁵ × 3³

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 864

List of positive integer factors of 864 that divides 854 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 854 and 864. The biggest common factor number is the GCF number.
So the greatest common factor 854 and 864 is 2.

Also check out the Least Common Multiple of 854 and 864