What is the Greatest Common Factor of 67138 and 67144?

Greatest common factor (GCF) of 67138 and 67144 is 2.

GCF(67138,67144) = 2

We will now calculate the prime factors of 67138 and 67144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67138 and 67144.

How to find the GCF of 67138 and 67144?

We will first find the prime factorization of 67138 and 67144. After we will calculate the factors of 67138 and 67144 and find the biggest common factor number .

Step-1: Prime Factorization of 67138

Prime factors of 67138 are 2, 33569. Prime factorization of 67138 in exponential form is:

67138 = 2¹ × 33569¹

Step-2: Prime Factorization of 67144

Prime factors of 67144 are 2, 7, 11, 109. Prime factorization of 67144 in exponential form is:

67144 = 2³ × 7¹ × 11¹ × 109¹

Step-3: Factors of 67138

List of positive integer factors of 67138 that divides 67138 without a remainder.

1, 2, 33569

Step-4: Factors of 67144

List of positive integer factors of 67144 that divides 67138 without a remainder.

1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 109, 154, 218, 308, 436, 616, 763, 872, 1199, 1526, 2398, 3052, 4796, 6104, 8393, 9592, 16786, 33572

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67138 and 67144. The biggest common factor number is the GCF number.
So the greatest common factor 67138 and 67144 is 2.

Also check out the Least Common Multiple of 67138 and 67144