What is the Greatest Common Factor of 17940 and 17953?

Greatest common factor (GCF) of 17940 and 17953 is 13.

GCF(17940,17953) = 13

We will now calculate the prime factors of 17940 and 17953, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17940 and 17953.

How to find the GCF of 17940 and 17953?

We will first find the prime factorization of 17940 and 17953. After we will calculate the factors of 17940 and 17953 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 17953

Prime factors of 17953 are 13, 1381. Prime factorization of 17953 in exponential form is:

17953 = 13¹ × 1381¹

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 17953

List of positive integer factors of 17953 that divides 17940 without a remainder.

1, 13, 1381

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17940 and 17953. The biggest common factor number is the GCF number.
So the greatest common factor 17940 and 17953 is 13.

Also check out the Least Common Multiple of 17940 and 17953