What is the Greatest Common Factor of 20565 and 20574?

Greatest common factor (GCF) of 20565 and 20574 is 9.

GCF(20565,20574) = 9

We will now calculate the prime factors of 20565 and 20574, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20565 and 20574.

How to find the GCF of 20565 and 20574?

We will first find the prime factorization of 20565 and 20574. After we will calculate the factors of 20565 and 20574 and find the biggest common factor number .

Step-1: Prime Factorization of 20565

Prime factors of 20565 are 3, 5, 457. Prime factorization of 20565 in exponential form is:

20565 = 3² × 5¹ × 457¹

Step-2: Prime Factorization of 20574

Prime factors of 20574 are 2, 3, 127. Prime factorization of 20574 in exponential form is:

20574 = 2¹ × 3⁴ × 127¹

Step-3: Factors of 20565

List of positive integer factors of 20565 that divides 20565 without a remainder.

1, 3, 5, 9, 15, 45, 457, 1371, 2285, 4113, 6855

Step-4: Factors of 20574

List of positive integer factors of 20574 that divides 20565 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 127, 162, 254, 381, 762, 1143, 2286, 3429, 6858, 10287

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20565 and 20574. The biggest common factor number is the GCF number.
So the greatest common factor 20565 and 20574 is 9.

Also check out the Least Common Multiple of 20565 and 20574