What is the Greatest Common Factor of 20580 and 20590?

Greatest common factor (GCF) of 20580 and 20590 is 10.

GCF(20580,20590) = 10

We will now calculate the prime factors of 20580 and 20590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20580 and 20590.

How to find the GCF of 20580 and 20590?

We will first find the prime factorization of 20580 and 20590. After we will calculate the factors of 20580 and 20590 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 20590

Prime factors of 20590 are 2, 5, 29, 71. Prime factorization of 20590 in exponential form is:

20590 = 2¹ × 5¹ × 29¹ × 71¹

Step-3: Factors of 20580

List of positive integer factors of 20580 that divides 20580 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

Step-4: Factors of 20590

List of positive integer factors of 20590 that divides 20580 without a remainder.

1, 2, 5, 10, 29, 58, 71, 142, 145, 290, 355, 710, 2059, 4118, 10295

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20580 and 20590. The biggest common factor number is the GCF number.
So the greatest common factor 20580 and 20590 is 10.

Also check out the Least Common Multiple of 20580 and 20590