What is the Greatest Common Factor of 67680 and 67697?

Greatest common factor (GCF) of 67680 and 67697 is 1.

GCF(67680,67697) = 1

We will now calculate the prime factors of 67680 and 67697, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67680 and 67697.

How to find the GCF of 67680 and 67697?

We will first find the prime factorization of 67680 and 67697. After we will calculate the factors of 67680 and 67697 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 67697

Prime factors of 67697 are 7, 19, 509. Prime factorization of 67697 in exponential form is:

67697 = 7¹ × 19¹ × 509¹

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 67697

List of positive integer factors of 67697 that divides 67680 without a remainder.

1, 7, 19, 133, 509, 3563, 9671

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67680 and 67697. The biggest common factor number is the GCF number.
So the greatest common factor 67680 and 67697 is 1.

Also check out the Least Common Multiple of 67680 and 67697