What is the Greatest Common Factor of 30709 and 30720?

Greatest common factor (GCF) of 30709 and 30720 is 1.

GCF(30709,30720) = 1

We will now calculate the prime factors of 30709 and 30720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30709 and 30720.

How to find the GCF of 30709 and 30720?

We will first find the prime factorization of 30709 and 30720. After we will calculate the factors of 30709 and 30720 and find the biggest common factor number .

Step-1: Prime Factorization of 30709

Prime factors of 30709 are 7, 41, 107. Prime factorization of 30709 in exponential form is:

30709 = 7¹ × 41¹ × 107¹

Step-2: Prime Factorization of 30720

Prime factors of 30720 are 2, 3, 5. Prime factorization of 30720 in exponential form is:

30720 = 2¹¹ × 3¹ × 5¹

Step-3: Factors of 30709

List of positive integer factors of 30709 that divides 30709 without a remainder.

1, 7, 41, 107, 287, 749, 4387

Step-4: Factors of 30720

List of positive integer factors of 30720 that divides 30709 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2048, 2560, 3072, 3840, 5120, 6144, 7680, 10240, 15360

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30709 and 30720. The biggest common factor number is the GCF number.
So the greatest common factor 30709 and 30720 is 1.

Also check out the Least Common Multiple of 30709 and 30720