What is the Greatest Common Factor of 30226 and 30240?

Greatest common factor (GCF) of 30226 and 30240 is 14.

GCF(30226,30240) = 14

We will now calculate the prime factors of 30226 and 30240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30226 and 30240.

How to find the GCF of 30226 and 30240?

We will first find the prime factorization of 30226 and 30240. After we will calculate the factors of 30226 and 30240 and find the biggest common factor number .

Step-1: Prime Factorization of 30226

Prime factors of 30226 are 2, 7, 17, 127. Prime factorization of 30226 in exponential form is:

30226 = 2¹ × 7¹ × 17¹ × 127¹

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 30226

List of positive integer factors of 30226 that divides 30226 without a remainder.

1, 2, 7, 14, 17, 34, 119, 127, 238, 254, 889, 1778, 2159, 4318, 15113

Step-4: Factors of 30240

List of positive integer factors of 30240 that divides 30226 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 30226 and 30240. The biggest common factor number is the GCF number.
So the greatest common factor 30226 and 30240 is 14.

Also check out the Least Common Multiple of 30226 and 30240