What is the Greatest Common Factor of 30221 and 30240?

Greatest common factor (GCF) of 30221 and 30240 is 1.

GCF(30221,30240) = 1

We will now calculate the prime factors of 30221 and 30240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30221 and 30240.

How to find the GCF of 30221 and 30240?

We will first find the prime factorization of 30221 and 30240. After we will calculate the factors of 30221 and 30240 and find the biggest common factor number .

Step-1: Prime Factorization of 30221

Prime factors of 30221 are 47, 643. Prime factorization of 30221 in exponential form is:

30221 = 47¹ × 643¹

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 30221

List of positive integer factors of 30221 that divides 30221 without a remainder.

1, 47, 643

Step-4: Factors of 30240

List of positive integer factors of 30240 that divides 30221 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 30221 and 30240. The biggest common factor number is the GCF number.
So the greatest common factor 30221 and 30240 is 1.

Also check out the Least Common Multiple of 30221 and 30240