What is the Greatest Common Factor of 20760 and 20775?

Greatest common factor (GCF) of 20760 and 20775 is 15.

GCF(20760,20775) = 15

We will now calculate the prime factors of 20760 and 20775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20760 and 20775.

How to find the GCF of 20760 and 20775?

We will first find the prime factorization of 20760 and 20775. After we will calculate the factors of 20760 and 20775 and find the biggest common factor number .

Step-1: Prime Factorization of 20760

Prime factors of 20760 are 2, 3, 5, 173. Prime factorization of 20760 in exponential form is:

20760 = 2³ × 3¹ × 5¹ × 173¹

Step-2: Prime Factorization of 20775

Prime factors of 20775 are 3, 5, 277. Prime factorization of 20775 in exponential form is:

20775 = 3¹ × 5² × 277¹

Step-3: Factors of 20760

List of positive integer factors of 20760 that divides 20760 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 173, 346, 519, 692, 865, 1038, 1384, 1730, 2076, 2595, 3460, 4152, 5190, 6920, 10380

Step-4: Factors of 20775

List of positive integer factors of 20775 that divides 20760 without a remainder.

1, 3, 5, 15, 25, 75, 277, 831, 1385, 4155, 6925

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20760 and 20775. The biggest common factor number is the GCF number.
So the greatest common factor 20760 and 20775 is 15.

Also check out the Least Common Multiple of 20760 and 20775