What is the Greatest Common Factor of 30240 and 30252?

Greatest common factor (GCF) of 30240 and 30252 is 12.

GCF(30240,30252) = 12

We will now calculate the prime factors of 30240 and 30252, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30240 and 30252.

How to find the GCF of 30240 and 30252?

We will first find the prime factorization of 30240 and 30252. After we will calculate the factors of 30240 and 30252 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30252

Prime factors of 30252 are 2, 3, 2521. Prime factorization of 30252 in exponential form is:

30252 = 2² × 3¹ × 2521¹

Step-3: Factors of 30240

List of positive integer factors of 30240 that divides 30240 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

Step-4: Factors of 30252

List of positive integer factors of 30252 that divides 30240 without a remainder.

1, 2, 3, 4, 6, 12, 2521, 5042, 7563, 10084, 15126

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30240 and 30252. The biggest common factor number is the GCF number.
So the greatest common factor 30240 and 30252 is 12.

Also check out the Least Common Multiple of 30240 and 30252