What is the Greatest Common Factor of 19685 and 19705?

Greatest common factor (GCF) of 19685 and 19705 is 5.

GCF(19685,19705) = 5

We will now calculate the prime factors of 19685 and 19705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19685 and 19705.

How to find the GCF of 19685 and 19705?

We will first find the prime factorization of 19685 and 19705. After we will calculate the factors of 19685 and 19705 and find the biggest common factor number .

Step-1: Prime Factorization of 19685

Prime factors of 19685 are 5, 31, 127. Prime factorization of 19685 in exponential form is:

19685 = 5¹ × 31¹ × 127¹

Step-2: Prime Factorization of 19705

Prime factors of 19705 are 5, 7, 563. Prime factorization of 19705 in exponential form is:

19705 = 5¹ × 7¹ × 563¹

Step-3: Factors of 19685

List of positive integer factors of 19685 that divides 19685 without a remainder.

1, 5, 31, 127, 155, 635, 3937

Step-4: Factors of 19705

List of positive integer factors of 19705 that divides 19685 without a remainder.

1, 5, 7, 35, 563, 2815, 3941

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19685 and 19705. The biggest common factor number is the GCF number.
So the greatest common factor 19685 and 19705 is 5.

Also check out the Least Common Multiple of 19685 and 19705