What is the Greatest Common Factor of 38709 and 38720?

Greatest common factor (GCF) of 38709 and 38720 is 11.

GCF(38709,38720) = 11

We will now calculate the prime factors of 38709 and 38720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38709 and 38720.

How to find the GCF of 38709 and 38720?

We will first find the prime factorization of 38709 and 38720. After we will calculate the factors of 38709 and 38720 and find the biggest common factor number .

Step-1: Prime Factorization of 38709

Prime factors of 38709 are 3, 11, 17, 23. Prime factorization of 38709 in exponential form is:

38709 = 3² × 11¹ × 17¹ × 23¹

Step-2: Prime Factorization of 38720

Prime factors of 38720 are 2, 5, 11. Prime factorization of 38720 in exponential form is:

38720 = 2⁶ × 5¹ × 11²

Step-3: Factors of 38709

List of positive integer factors of 38709 that divides 38709 without a remainder.

1, 3, 9, 11, 17, 23, 33, 51, 69, 99, 153, 187, 207, 253, 391, 561, 759, 1173, 1683, 2277, 3519, 4301, 12903

Step-4: Factors of 38720

List of positive integer factors of 38720 that divides 38709 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 64, 80, 88, 110, 121, 160, 176, 220, 242, 320, 352, 440, 484, 605, 704, 880, 968, 1210, 1760, 1936, 2420, 3520, 3872, 4840, 7744, 9680, 19360

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38709 and 38720. The biggest common factor number is the GCF number.
So the greatest common factor 38709 and 38720 is 11.

Also check out the Least Common Multiple of 38709 and 38720