What is the Greatest Common Factor of 20208 and 20224?

Greatest common factor (GCF) of 20208 and 20224 is 16.

GCF(20208,20224) = 16

We will now calculate the prime factors of 20208 and 20224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20208 and 20224.

How to find the GCF of 20208 and 20224?

We will first find the prime factorization of 20208 and 20224. After we will calculate the factors of 20208 and 20224 and find the biggest common factor number .

Step-1: Prime Factorization of 20208

Prime factors of 20208 are 2, 3, 421. Prime factorization of 20208 in exponential form is:

20208 = 2⁴ × 3¹ × 421¹

Step-2: Prime Factorization of 20224

Prime factors of 20224 are 2, 79. Prime factorization of 20224 in exponential form is:

20224 = 2⁸ × 79¹

Step-3: Factors of 20208

List of positive integer factors of 20208 that divides 20208 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 421, 842, 1263, 1684, 2526, 3368, 5052, 6736, 10104

Step-4: Factors of 20224

List of positive integer factors of 20224 that divides 20208 without a remainder.

1, 2, 4, 8, 16, 32, 64, 79, 128, 158, 256, 316, 632, 1264, 2528, 5056, 10112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20208 and 20224. The biggest common factor number is the GCF number.
So the greatest common factor 20208 and 20224 is 16.

Also check out the Least Common Multiple of 20208 and 20224