What is the Greatest Common Factor of 840 and 854?

Greatest common factor (GCF) of 840 and 854 is 14.

GCF(840,854) = 14

We will now calculate the prime factors of 840 and 854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 840 and 854.

How to find the GCF of 840 and 854?

We will first find the prime factorization of 840 and 854. After we will calculate the factors of 840 and 854 and find the biggest common factor number .

Step-1: Prime Factorization of 840

Prime factors of 840 are 2, 3, 5, 7. Prime factorization of 840 in exponential form is:

840 = 2³ × 3¹ × 5¹ × 7¹

Step-2: 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-3: Factors of 840

List of positive integer factors of 840 that divides 840 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420

Step-4: Factors of 854

List of positive integer factors of 854 that divides 840 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 840 and 854. The biggest common factor number is the GCF number.
So the greatest common factor 840 and 854 is 14.

Also check out the Least Common Multiple of 840 and 854