What is the Greatest Common Factor of 854 and 861?

Greatest common factor (GCF) of 854 and 861 is 7.

GCF(854,861) = 7

We will now calculate the prime factors of 854 and 861, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 854 and 861.

How to find the GCF of 854 and 861?

We will first find the prime factorization of 854 and 861. After we will calculate the factors of 854 and 861 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 861

Prime factors of 861 are 3, 7, 41. Prime factorization of 861 in exponential form is:

861 = 3¹ × 7¹ × 41¹

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 861

List of positive integer factors of 861 that divides 854 without a remainder.

1, 3, 7, 21, 41, 123, 287

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 854 and 861. The biggest common factor number is the GCF number.
So the greatest common factor 854 and 861 is 7.

Also check out the Least Common Multiple of 854 and 861