What is the Greatest Common Factor of 28224 and 28231?

Greatest common factor (GCF) of 28224 and 28231 is 7.

GCF(28224,28231) = 7

We will now calculate the prime factors of 28224 and 28231, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28224 and 28231.

How to find the GCF of 28224 and 28231?

We will first find the prime factorization of 28224 and 28231. After we will calculate the factors of 28224 and 28231 and find the biggest common factor number .

Step-1: Prime Factorization of 28224

Prime factors of 28224 are 2, 3, 7. Prime factorization of 28224 in exponential form is:

28224 = 2⁶ × 3² × 7²

Step-2: Prime Factorization of 28231

Prime factors of 28231 are 7, 37, 109. Prime factorization of 28231 in exponential form is:

28231 = 7¹ × 37¹ × 109¹

Step-3: Factors of 28224

List of positive integer factors of 28224 that divides 28224 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 49, 56, 63, 64, 72, 84, 96, 98, 112, 126, 144, 147, 168, 192, 196, 224, 252, 288, 294, 336, 392, 441, 448, 504, 576, 588, 672, 784, 882, 1008, 1176, 1344, 1568, 1764, 2016, 2352, 3136, 3528, 4032, 4704, 7056, 9408, 14112

Step-4: Factors of 28231

List of positive integer factors of 28231 that divides 28224 without a remainder.

1, 7, 37, 109, 259, 763, 4033

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28224 and 28231. The biggest common factor number is the GCF number.
So the greatest common factor 28224 and 28231 is 7.

Also check out the Least Common Multiple of 28224 and 28231