What is the Greatest Common Factor of 20574 and 20580?

Greatest common factor (GCF) of 20574 and 20580 is 6.

GCF(20574,20580) = 6

We will now calculate the prime factors of 20574 and 20580, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20574 and 20580.

How to find the GCF of 20574 and 20580?

We will first find the prime factorization of 20574 and 20580. After we will calculate the factors of 20574 and 20580 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 20580

Prime factors of 20580 are 2, 3, 5, 7. Prime factorization of 20580 in exponential form is:

20580 = 2² × 3¹ × 5¹ × 7³

Step-3: Factors of 20574

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

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

Step-4: Factors of 20580

List of positive integer factors of 20580 that divides 20574 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 49, 60, 70, 84, 98, 105, 140, 147, 196, 210, 245, 294, 343, 420, 490, 588, 686, 735, 980, 1029, 1372, 1470, 1715, 2058, 2940, 3430, 4116, 5145, 6860, 10290

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20574 and 20580. The biggest common factor number is the GCF number.
So the greatest common factor 20574 and 20580 is 6.

Also check out the Least Common Multiple of 20574 and 20580