What is the Greatest Common Factor of 20905 and 20925?

Greatest common factor (GCF) of 20905 and 20925 is 5.

GCF(20905,20925) = 5

We will now calculate the prime factors of 20905 and 20925, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20905 and 20925.

How to find the GCF of 20905 and 20925?

We will first find the prime factorization of 20905 and 20925. After we will calculate the factors of 20905 and 20925 and find the biggest common factor number .

Step-1: Prime Factorization of 20905

Prime factors of 20905 are 5, 37, 113. Prime factorization of 20905 in exponential form is:

20905 = 5¹ × 37¹ × 113¹

Step-2: Prime Factorization of 20925

Prime factors of 20925 are 3, 5, 31. Prime factorization of 20925 in exponential form is:

20925 = 3³ × 5² × 31¹

Step-3: Factors of 20905

List of positive integer factors of 20905 that divides 20905 without a remainder.

1, 5, 37, 113, 185, 565, 4181

Step-4: Factors of 20925

List of positive integer factors of 20925 that divides 20905 without a remainder.

1, 3, 5, 9, 15, 25, 27, 31, 45, 75, 93, 135, 155, 225, 279, 465, 675, 775, 837, 1395, 2325, 4185, 6975

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20905 and 20925. The biggest common factor number is the GCF number.
So the greatest common factor 20905 and 20925 is 5.

Also check out the Least Common Multiple of 20905 and 20925