What is the Greatest Common Factor of 30229 and 30240?

Greatest common factor (GCF) of 30229 and 30240 is 1.

GCF(30229,30240) = 1

We will now calculate the prime factors of 30229 and 30240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30229 and 30240.

How to find the GCF of 30229 and 30240?

We will first find the prime factorization of 30229 and 30240. After we will calculate the factors of 30229 and 30240 and find the biggest common factor number .

Step-1: Prime Factorization of 30229

Prime factors of 30229 are 19, 37, 43. Prime factorization of 30229 in exponential form is:

30229 = 19¹ × 37¹ × 43¹

Step-2: Prime Factorization of 30240

Prime factors of 30240 are 2, 3, 5, 7. Prime factorization of 30240 in exponential form is:

30240 = 2⁵ × 3³ × 5¹ × 7¹

Step-3: Factors of 30229

List of positive integer factors of 30229 that divides 30229 without a remainder.

1, 19, 37, 43, 703, 817, 1591

Step-4: Factors of 30240

List of positive integer factors of 30240 that divides 30229 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 108, 112, 120, 126, 135, 140, 144, 160, 168, 180, 189, 210, 216, 224, 240, 252, 270, 280, 288, 315, 336, 360, 378, 420, 432, 480, 504, 540, 560, 630, 672, 720, 756, 840, 864, 945, 1008, 1080, 1120, 1260, 1440, 1512, 1680, 1890, 2016, 2160, 2520, 3024, 3360, 3780, 4320, 5040, 6048, 7560, 10080, 15120

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30229 and 30240. The biggest common factor number is the GCF number.
So the greatest common factor 30229 and 30240 is 1.

Also check out the Least Common Multiple of 30229 and 30240