What is the Greatest Common Factor of 67104 and 67116?

Greatest common factor (GCF) of 67104 and 67116 is 12.

GCF(67104,67116) = 12

We will now calculate the prime factors of 67104 and 67116, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67104 and 67116.

How to find the GCF of 67104 and 67116?

We will first find the prime factorization of 67104 and 67116. After we will calculate the factors of 67104 and 67116 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 67116

Prime factors of 67116 are 2, 3, 7, 17, 47. Prime factorization of 67116 in exponential form is:

67116 = 2² × 3¹ × 7¹ × 17¹ × 47¹

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 67116

List of positive integer factors of 67116 that divides 67104 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 47, 51, 68, 84, 94, 102, 119, 141, 188, 204, 238, 282, 329, 357, 476, 564, 658, 714, 799, 987, 1316, 1428, 1598, 1974, 2397, 3196, 3948, 4794, 5593, 9588, 11186, 16779, 22372, 33558

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67104 and 67116. The biggest common factor number is the GCF number.
So the greatest common factor 67104 and 67116 is 12.

Also check out the Least Common Multiple of 67104 and 67116