What is the Greatest Common Factor of 17940 and 17960?

Greatest common factor (GCF) of 17940 and 17960 is 20.

GCF(17940,17960) = 20

We will now calculate the prime factors of 17940 and 17960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17940 and 17960.

How to find the GCF of 17940 and 17960?

We will first find the prime factorization of 17940 and 17960. After we will calculate the factors of 17940 and 17960 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17960

Prime factors of 17960 are 2, 5, 449. Prime factorization of 17960 in exponential form is:

17960 = 2³ × 5¹ × 449¹

Step-3: Factors of 17940

List of positive integer factors of 17940 that divides 17940 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

Step-4: Factors of 17960

List of positive integer factors of 17960 that divides 17940 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 449, 898, 1796, 2245, 3592, 4490, 8980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17940 and 17960. The biggest common factor number is the GCF number.
So the greatest common factor 17940 and 17960 is 20.

Also check out the Least Common Multiple of 17940 and 17960