What is the Greatest Common Factor of 67680 and 67692?

Greatest common factor (GCF) of 67680 and 67692 is 12.

GCF(67680,67692) = 12

We will now calculate the prime factors of 67680 and 67692, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67680 and 67692.

How to find the GCF of 67680 and 67692?

We will first find the prime factorization of 67680 and 67692. After we will calculate the factors of 67680 and 67692 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 67692

Prime factors of 67692 are 2, 3, 5641. Prime factorization of 67692 in exponential form is:

67692 = 2² × 3¹ × 5641¹

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 67692

List of positive integer factors of 67692 that divides 67680 without a remainder.

1, 2, 3, 4, 6, 12, 5641, 11282, 16923, 22564, 33846

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67680 and 67692. The biggest common factor number is the GCF number.
So the greatest common factor 67680 and 67692 is 12.

Also check out the Least Common Multiple of 67680 and 67692