What is the Greatest Common Factor of 28210 and 28224?

Greatest common factor (GCF) of 28210 and 28224 is 14.

GCF(28210,28224) = 14

We will now calculate the prime factors of 28210 and 28224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28210 and 28224.

How to find the GCF of 28210 and 28224?

We will first find the prime factorization of 28210 and 28224. After we will calculate the factors of 28210 and 28224 and find the biggest common factor number .

Step-1: Prime Factorization of 28210

Prime factors of 28210 are 2, 5, 7, 13, 31. Prime factorization of 28210 in exponential form is:

28210 = 2¹ × 5¹ × 7¹ × 13¹ × 31¹

Step-2: 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-3: Factors of 28210

List of positive integer factors of 28210 that divides 28210 without a remainder.

1, 2, 5, 7, 10, 13, 14, 26, 31, 35, 62, 65, 70, 91, 130, 155, 182, 217, 310, 403, 434, 455, 806, 910, 1085, 2015, 2170, 2821, 4030, 5642, 14105

Step-4: Factors of 28224

List of positive integer factors of 28224 that divides 28210 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28210 and 28224. The biggest common factor number is the GCF number.
So the greatest common factor 28210 and 28224 is 14.

Also check out the Least Common Multiple of 28210 and 28224