What is the Greatest Common Factor of 17920 and 17940?

Greatest common factor (GCF) of 17920 and 17940 is 20.

GCF(17920,17940) = 20

We will now calculate the prime factors of 17920 and 17940, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17920 and 17940.

How to find the GCF of 17920 and 17940?

We will first find the prime factorization of 17920 and 17940. After we will calculate the factors of 17920 and 17940 and find the biggest common factor number .

Step-1: Prime Factorization of 17920

Prime factors of 17920 are 2, 5, 7. Prime factorization of 17920 in exponential form is:

17920 = 2⁹ × 5¹ × 7¹

Step-2: Prime Factorization of 17940

Prime factors of 17940 are 2, 3, 5, 13, 23. Prime factorization of 17940 in exponential form is:

17940 = 2² × 3¹ × 5¹ × 13¹ × 23¹

Step-3: Factors of 17920

List of positive integer factors of 17920 that divides 17920 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 128, 140, 160, 224, 256, 280, 320, 448, 512, 560, 640, 896, 1120, 1280, 1792, 2240, 2560, 3584, 4480, 8960

Step-4: Factors of 17940

List of positive integer factors of 17940 that divides 17920 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 23, 26, 30, 39, 46, 52, 60, 65, 69, 78, 92, 115, 130, 138, 156, 195, 230, 260, 276, 299, 345, 390, 460, 598, 690, 780, 897, 1196, 1380, 1495, 1794, 2990, 3588, 4485, 5980, 8970

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17920 and 17940. The biggest common factor number is the GCF number.
So the greatest common factor 17920 and 17940 is 20.

Also check out the Least Common Multiple of 17920 and 17940