What is the Greatest Common Factor of 67696 and 67704?

Greatest common factor (GCF) of 67696 and 67704 is 8.

GCF(67696,67704) = 8

We will now calculate the prime factors of 67696 and 67704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67696 and 67704.

How to find the GCF of 67696 and 67704?

We will first find the prime factorization of 67696 and 67704. After we will calculate the factors of 67696 and 67704 and find the biggest common factor number .

Step-1: Prime Factorization of 67696

Prime factors of 67696 are 2, 4231. Prime factorization of 67696 in exponential form is:

67696 = 2⁴ × 4231¹

Step-2: Prime Factorization of 67704

Prime factors of 67704 are 2, 3, 7, 13, 31. Prime factorization of 67704 in exponential form is:

67704 = 2³ × 3¹ × 7¹ × 13¹ × 31¹

Step-3: Factors of 67696

List of positive integer factors of 67696 that divides 67696 without a remainder.

1, 2, 4, 8, 16, 4231, 8462, 16924, 33848

Step-4: Factors of 67704

List of positive integer factors of 67704 that divides 67696 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 31, 39, 42, 52, 56, 62, 78, 84, 91, 93, 104, 124, 156, 168, 182, 186, 217, 248, 273, 312, 364, 372, 403, 434, 546, 651, 728, 744, 806, 868, 1092, 1209, 1302, 1612, 1736, 2184, 2418, 2604, 2821, 3224, 4836, 5208, 5642, 8463, 9672, 11284, 16926, 22568, 33852

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67696 and 67704. The biggest common factor number is the GCF number.
So the greatest common factor 67696 and 67704 is 8.

Also check out the Least Common Multiple of 67696 and 67704