What is the Greatest Common Factor of 20806 and 20825?

Greatest common factor (GCF) of 20806 and 20825 is 1.

GCF(20806,20825) = 1

We will now calculate the prime factors of 20806 and 20825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20806 and 20825.

How to find the GCF of 20806 and 20825?

We will first find the prime factorization of 20806 and 20825. After we will calculate the factors of 20806 and 20825 and find the biggest common factor number .

Step-1: Prime Factorization of 20806

Prime factors of 20806 are 2, 101, 103. Prime factorization of 20806 in exponential form is:

20806 = 2¹ × 101¹ × 103¹

Step-2: Prime Factorization of 20825

Prime factors of 20825 are 5, 7, 17. Prime factorization of 20825 in exponential form is:

20825 = 5² × 7² × 17¹

Step-3: Factors of 20806

List of positive integer factors of 20806 that divides 20806 without a remainder.

1, 2, 101, 103, 202, 206, 10403

Step-4: Factors of 20825

List of positive integer factors of 20825 that divides 20806 without a remainder.

1, 5, 7, 17, 25, 35, 49, 85, 119, 175, 245, 425, 595, 833, 1225, 2975, 4165

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20806 and 20825. The biggest common factor number is the GCF number.
So the greatest common factor 20806 and 20825 is 1.

Also check out the Least Common Multiple of 20806 and 20825