What is the Greatest Common Factor of 67125 and 67144?

Greatest common factor (GCF) of 67125 and 67144 is 1.

GCF(67125,67144) = 1

We will now calculate the prime factors of 67125 and 67144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67125 and 67144.

How to find the GCF of 67125 and 67144?

We will first find the prime factorization of 67125 and 67144. After we will calculate the factors of 67125 and 67144 and find the biggest common factor number .

Step-1: Prime Factorization of 67125

Prime factors of 67125 are 3, 5, 179. Prime factorization of 67125 in exponential form is:

67125 = 3¹ × 5³ × 179¹

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 67125

List of positive integer factors of 67125 that divides 67125 without a remainder.

1, 3, 5, 15, 25, 75, 125, 179, 375, 537, 895, 2685, 4475, 13425, 22375

Step-4: Factors of 67144

List of positive integer factors of 67144 that divides 67125 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 67125 and 67144. The biggest common factor number is the GCF number.
So the greatest common factor 67125 and 67144 is 1.

Also check out the Least Common Multiple of 67125 and 67144