What is the Greatest Common Factor of 67104 and 67122?

Greatest common factor (GCF) of 67104 and 67122 is 18.

GCF(67104,67122) = 18

We will now calculate the prime factors of 67104 and 67122, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67104 and 67122.

How to find the GCF of 67104 and 67122?

We will first find the prime factorization of 67104 and 67122. After we will calculate the factors of 67104 and 67122 and find the biggest common factor number .

Step-1: Prime Factorization of 67104

Prime factors of 67104 are 2, 3, 233. Prime factorization of 67104 in exponential form is:

67104 = 2⁵ × 3² × 233¹

Step-2: Prime Factorization of 67122

Prime factors of 67122 are 2, 3, 11, 113. Prime factorization of 67122 in exponential form is:

67122 = 2¹ × 3³ × 11¹ × 113¹

Step-3: Factors of 67104

List of positive integer factors of 67104 that divides 67104 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 233, 288, 466, 699, 932, 1398, 1864, 2097, 2796, 3728, 4194, 5592, 7456, 8388, 11184, 16776, 22368, 33552

Step-4: Factors of 67122

List of positive integer factors of 67122 that divides 67104 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 99, 113, 198, 226, 297, 339, 594, 678, 1017, 1243, 2034, 2486, 3051, 3729, 6102, 7458, 11187, 22374, 33561

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67104 and 67122. The biggest common factor number is the GCF number.
So the greatest common factor 67104 and 67122 is 18.

Also check out the Least Common Multiple of 67104 and 67122