What is the Greatest Common Factor of 67665 and 67680?

Greatest common factor (GCF) of 67665 and 67680 is 15.

GCF(67665,67680) = 15

We will now calculate the prime factors of 67665 and 67680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67665 and 67680.

How to find the GCF of 67665 and 67680?

We will first find the prime factorization of 67665 and 67680. After we will calculate the factors of 67665 and 67680 and find the biggest common factor number .

Step-1: Prime Factorization of 67665

Prime factors of 67665 are 3, 5, 13, 347. Prime factorization of 67665 in exponential form is:

67665 = 3¹ × 5¹ × 13¹ × 347¹

Step-2: 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-3: Factors of 67665

List of positive integer factors of 67665 that divides 67665 without a remainder.

1, 3, 5, 13, 15, 39, 65, 195, 347, 1041, 1735, 4511, 5205, 13533, 22555

Step-4: Factors of 67680

List of positive integer factors of 67680 that divides 67665 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67665 and 67680. The biggest common factor number is the GCF number.
So the greatest common factor 67665 and 67680 is 15.

Also check out the Least Common Multiple of 67665 and 67680