What is the Greatest Common Factor of 23198 and 23205?

Greatest common factor (GCF) of 23198 and 23205 is 7.

GCF(23198,23205) = 7

We will now calculate the prime factors of 23198 and 23205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23198 and 23205.

How to find the GCF of 23198 and 23205?

We will first find the prime factorization of 23198 and 23205. After we will calculate the factors of 23198 and 23205 and find the biggest common factor number .

Step-1: Prime Factorization of 23198

Prime factors of 23198 are 2, 7, 1657. Prime factorization of 23198 in exponential form is:

23198 = 2¹ × 7¹ × 1657¹

Step-2: Prime Factorization of 23205

Prime factors of 23205 are 3, 5, 7, 13, 17. Prime factorization of 23205 in exponential form is:

23205 = 3¹ × 5¹ × 7¹ × 13¹ × 17¹

Step-3: Factors of 23198

List of positive integer factors of 23198 that divides 23198 without a remainder.

1, 2, 7, 14, 1657, 3314, 11599

Step-4: Factors of 23205

List of positive integer factors of 23205 that divides 23198 without a remainder.

1, 3, 5, 7, 13, 15, 17, 21, 35, 39, 51, 65, 85, 91, 105, 119, 195, 221, 255, 273, 357, 455, 595, 663, 1105, 1365, 1547, 1785, 3315, 4641, 7735

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23198 and 23205. The biggest common factor number is the GCF number.
So the greatest common factor 23198 and 23205 is 7.

Also check out the Least Common Multiple of 23198 and 23205