What is the Greatest Common Factor of 67838 and 67854?

Greatest common factor (GCF) of 67838 and 67854 is 2.

GCF(67838,67854) = 2

We will now calculate the prime factors of 67838 and 67854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67838 and 67854.

How to find the GCF of 67838 and 67854?

We will first find the prime factorization of 67838 and 67854. After we will calculate the factors of 67838 and 67854 and find the biggest common factor number .

Step-1: Prime Factorization of 67838

Prime factors of 67838 are 2, 107, 317. Prime factorization of 67838 in exponential form is:

67838 = 2¹ × 107¹ × 317¹

Step-2: Prime Factorization of 67854

Prime factors of 67854 are 2, 3, 43, 263. Prime factorization of 67854 in exponential form is:

67854 = 2¹ × 3¹ × 43¹ × 263¹

Step-3: Factors of 67838

List of positive integer factors of 67838 that divides 67838 without a remainder.

1, 2, 107, 214, 317, 634, 33919

Step-4: Factors of 67854

List of positive integer factors of 67854 that divides 67838 without a remainder.

1, 2, 3, 6, 43, 86, 129, 258, 263, 526, 789, 1578, 11309, 22618, 33927

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67838 and 67854. The biggest common factor number is the GCF number.
So the greatest common factor 67838 and 67854 is 2.

Also check out the Least Common Multiple of 67838 and 67854