What is the Greatest Common Factor of 20705 and 20725?

Greatest common factor (GCF) of 20705 and 20725 is 5.

GCF(20705,20725) = 5

We will now calculate the prime factors of 20705 and 20725, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20705 and 20725.

How to find the GCF of 20705 and 20725?

We will first find the prime factorization of 20705 and 20725. After we will calculate the factors of 20705 and 20725 and find the biggest common factor number .

Step-1: Prime Factorization of 20705

Prime factors of 20705 are 5, 41, 101. Prime factorization of 20705 in exponential form is:

20705 = 5¹ × 41¹ × 101¹

Step-2: Prime Factorization of 20725

Prime factors of 20725 are 5, 829. Prime factorization of 20725 in exponential form is:

20725 = 5² × 829¹

Step-3: Factors of 20705

List of positive integer factors of 20705 that divides 20705 without a remainder.

1, 5, 41, 101, 205, 505, 4141

Step-4: Factors of 20725

List of positive integer factors of 20725 that divides 20705 without a remainder.

1, 5, 25, 829, 4145

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20705 and 20725. The biggest common factor number is the GCF number.
So the greatest common factor 20705 and 20725 is 5.

Also check out the Least Common Multiple of 20705 and 20725