What is the Greatest Common Factor of 67294 and 67312?

Greatest common factor (GCF) of 67294 and 67312 is 2.

GCF(67294,67312) = 2

We will now calculate the prime factors of 67294 and 67312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67294 and 67312.

How to find the GCF of 67294 and 67312?

We will first find the prime factorization of 67294 and 67312. After we will calculate the factors of 67294 and 67312 and find the biggest common factor number .

Step-1: Prime Factorization of 67294

Prime factors of 67294 are 2, 33647. Prime factorization of 67294 in exponential form is:

67294 = 2¹ × 33647¹

Step-2: Prime Factorization of 67312

Prime factors of 67312 are 2, 7, 601. Prime factorization of 67312 in exponential form is:

67312 = 2⁴ × 7¹ × 601¹

Step-3: Factors of 67294

List of positive integer factors of 67294 that divides 67294 without a remainder.

1, 2, 33647

Step-4: Factors of 67312

List of positive integer factors of 67312 that divides 67294 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 601, 1202, 2404, 4207, 4808, 8414, 9616, 16828, 33656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67294 and 67312. The biggest common factor number is the GCF number.
So the greatest common factor 67294 and 67312 is 2.

Also check out the Least Common Multiple of 67294 and 67312