What is the Greatest Common Factor of 19674 and 19680?

Greatest common factor (GCF) of 19674 and 19680 is 6.

GCF(19674,19680) = 6

We will now calculate the prime factors of 19674 and 19680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19674 and 19680.

How to find the GCF of 19674 and 19680?

We will first find the prime factorization of 19674 and 19680. After we will calculate the factors of 19674 and 19680 and find the biggest common factor number .

Step-1: Prime Factorization of 19674

Prime factors of 19674 are 2, 3, 1093. Prime factorization of 19674 in exponential form is:

19674 = 2¹ × 3² × 1093¹

Step-2: Prime Factorization of 19680

Prime factors of 19680 are 2, 3, 5, 41. Prime factorization of 19680 in exponential form is:

19680 = 2⁵ × 3¹ × 5¹ × 41¹

Step-3: Factors of 19674

List of positive integer factors of 19674 that divides 19674 without a remainder.

1, 2, 3, 6, 9, 18, 1093, 2186, 3279, 6558, 9837

Step-4: Factors of 19680

List of positive integer factors of 19680 that divides 19674 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 41, 48, 60, 80, 82, 96, 120, 123, 160, 164, 205, 240, 246, 328, 410, 480, 492, 615, 656, 820, 984, 1230, 1312, 1640, 1968, 2460, 3280, 3936, 4920, 6560, 9840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19674 and 19680. The biggest common factor number is the GCF number.
So the greatest common factor 19674 and 19680 is 6.

Also check out the Least Common Multiple of 19674 and 19680