What is the Greatest Common Factor of 17940 and 17946?

Greatest common factor (GCF) of 17940 and 17946 is 6.

GCF(17940,17946) = 6

We will now calculate the prime factors of 17940 and 17946, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17940 and 17946.

How to find the GCF of 17940 and 17946?

We will first find the prime factorization of 17940 and 17946. After we will calculate the factors of 17940 and 17946 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 17946

Prime factors of 17946 are 2, 3, 997. Prime factorization of 17946 in exponential form is:

17946 = 2¹ × 3² × 997¹

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 17946

List of positive integer factors of 17946 that divides 17940 without a remainder.

1, 2, 3, 6, 9, 18, 997, 1994, 2991, 5982, 8973

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17940 and 17946. The biggest common factor number is the GCF number.
So the greatest common factor 17940 and 17946 is 6.

Also check out the Least Common Multiple of 17940 and 17946