What is the Greatest Common Factor of 840 and 849?

Greatest common factor (GCF) of 840 and 849 is 3.

GCF(840,849) = 3

We will now calculate the prime factors of 840 and 849, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 840 and 849.

How to find the GCF of 840 and 849?

We will first find the prime factorization of 840 and 849. After we will calculate the factors of 840 and 849 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 849

Prime factors of 849 are 3, 283. Prime factorization of 849 in exponential form is:

849 = 3¹ × 283¹

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 849

List of positive integer factors of 849 that divides 840 without a remainder.

1, 3, 283

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 840 and 849. The biggest common factor number is the GCF number.
So the greatest common factor 840 and 849 is 3.

Also check out the Least Common Multiple of 840 and 849