What is the Greatest Common Factor of 19705 and 19720?

Greatest common factor (GCF) of 19705 and 19720 is 5.

GCF(19705,19720) = 5

We will now calculate the prime factors of 19705 and 19720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19705 and 19720.

How to find the GCF of 19705 and 19720?

We will first find the prime factorization of 19705 and 19720. After we will calculate the factors of 19705 and 19720 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19720

Prime factors of 19720 are 2, 5, 17, 29. Prime factorization of 19720 in exponential form is:

19720 = 2³ × 5¹ × 17¹ × 29¹

Step-3: Factors of 19705

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

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

Step-4: Factors of 19720

List of positive integer factors of 19720 that divides 19705 without a remainder.

1, 2, 4, 5, 8, 10, 17, 20, 29, 34, 40, 58, 68, 85, 116, 136, 145, 170, 232, 290, 340, 493, 580, 680, 986, 1160, 1972, 2465, 3944, 4930, 9860

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19705 and 19720. The biggest common factor number is the GCF number.
So the greatest common factor 19705 and 19720 is 5.

Also check out the Least Common Multiple of 19705 and 19720