What is the Greatest Common Factor of 67312 and 67319?

Greatest common factor (GCF) of 67312 and 67319 is 7.

GCF(67312,67319) = 7

We will now calculate the prime factors of 67312 and 67319, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67312 and 67319.

How to find the GCF of 67312 and 67319?

We will first find the prime factorization of 67312 and 67319. After we will calculate the factors of 67312 and 67319 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 67319

Prime factors of 67319 are 7, 59, 163. Prime factorization of 67319 in exponential form is:

67319 = 7¹ × 59¹ × 163¹

Step-3: Factors of 67312

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

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

Step-4: Factors of 67319

List of positive integer factors of 67319 that divides 67312 without a remainder.

1, 7, 59, 163, 413, 1141, 9617

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67312 and 67319. The biggest common factor number is the GCF number.
So the greatest common factor 67312 and 67319 is 7.

Also check out the Least Common Multiple of 67312 and 67319