What is the Greatest Common Factor of 17730 and 17740?

Greatest common factor (GCF) of 17730 and 17740 is 10.

GCF(17730,17740) = 10

We will now calculate the prime factors of 17730 and 17740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17730 and 17740.

How to find the GCF of 17730 and 17740?

We will first find the prime factorization of 17730 and 17740. After we will calculate the factors of 17730 and 17740 and find the biggest common factor number .

Step-1: Prime Factorization of 17730

Prime factors of 17730 are 2, 3, 5, 197. Prime factorization of 17730 in exponential form is:

17730 = 2¹ × 3² × 5¹ × 197¹

Step-2: Prime Factorization of 17740

Prime factors of 17740 are 2, 5, 887. Prime factorization of 17740 in exponential form is:

17740 = 2² × 5¹ × 887¹

Step-3: Factors of 17730

List of positive integer factors of 17730 that divides 17730 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 197, 394, 591, 985, 1182, 1773, 1970, 2955, 3546, 5910, 8865

Step-4: Factors of 17740

List of positive integer factors of 17740 that divides 17730 without a remainder.

1, 2, 4, 5, 10, 20, 887, 1774, 3548, 4435, 8870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17730 and 17740. The biggest common factor number is the GCF number.
So the greatest common factor 17730 and 17740 is 10.

Also check out the Least Common Multiple of 17730 and 17740