What is the Greatest Common Factor of 838 and 848?

Greatest common factor (GCF) of 838 and 848 is 2.

GCF(838,848) = 2

We will now calculate the prime factors of 838 and 848, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 838 and 848.

How to find the GCF of 838 and 848?

We will first find the prime factorization of 838 and 848. After we will calculate the factors of 838 and 848 and find the biggest common factor number .

Step-1: Prime Factorization of 838

Prime factors of 838 are 2, 419. Prime factorization of 838 in exponential form is:

838 = 2¹ × 419¹

Step-2: Prime Factorization of 848

Prime factors of 848 are 2, 53. Prime factorization of 848 in exponential form is:

848 = 2⁴ × 53¹

Step-3: Factors of 838

List of positive integer factors of 838 that divides 838 without a remainder.

1, 2, 419

Step-4: Factors of 848

List of positive integer factors of 848 that divides 838 without a remainder.

1, 2, 4, 8, 16, 53, 106, 212, 424

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 838 and 848. The biggest common factor number is the GCF number.
So the greatest common factor 838 and 848 is 2.

Also check out the Least Common Multiple of 838 and 848