What is the Greatest Common Factor of 67680 and 67696?

Greatest common factor (GCF) of 67680 and 67696 is 16.

GCF(67680,67696) = 16

We will now calculate the prime factors of 67680 and 67696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67680 and 67696.

How to find the GCF of 67680 and 67696?

We will first find the prime factorization of 67680 and 67696. After we will calculate the factors of 67680 and 67696 and find the biggest common factor number .

Step-1: Prime Factorization of 67680

Prime factors of 67680 are 2, 3, 5, 47. Prime factorization of 67680 in exponential form is:

67680 = 2⁵ × 3² × 5¹ × 47¹

Step-2: Prime Factorization of 67696

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

67696 = 2⁴ × 4231¹

Step-3: Factors of 67680

List of positive integer factors of 67680 that divides 67680 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 47, 48, 60, 72, 80, 90, 94, 96, 120, 141, 144, 160, 180, 188, 235, 240, 282, 288, 360, 376, 423, 470, 480, 564, 705, 720, 752, 846, 940, 1128, 1410, 1440, 1504, 1692, 1880, 2115, 2256, 2820, 3384, 3760, 4230, 4512, 5640, 6768, 7520, 8460, 11280, 13536, 16920, 22560, 33840

Step-4: Factors of 67696

List of positive integer factors of 67696 that divides 67680 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67680 and 67696. The biggest common factor number is the GCF number.
So the greatest common factor 67680 and 67696 is 16.

Also check out the Least Common Multiple of 67680 and 67696