What is the Greatest Common Factor of 17940 and 17949?

Greatest common factor (GCF) of 17940 and 17949 is 3.

GCF(17940,17949) = 3

We will now calculate the prime factors of 17940 and 17949, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17940 and 17949.

How to find the GCF of 17940 and 17949?

We will first find the prime factorization of 17940 and 17949. After we will calculate the factors of 17940 and 17949 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 17949

Prime factors of 17949 are 3, 31, 193. Prime factorization of 17949 in exponential form is:

17949 = 3¹ × 31¹ × 193¹

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 17949

List of positive integer factors of 17949 that divides 17940 without a remainder.

1, 3, 31, 93, 193, 579, 5983

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17940 and 17949. The biggest common factor number is the GCF number.
So the greatest common factor 17940 and 17949 is 3.

Also check out the Least Common Multiple of 17940 and 17949