What is the Greatest Common Factor of 10224 and 10240?

Greatest common factor (GCF) of 10224 and 10240 is 16.

GCF(10224,10240) = 16

We will now calculate the prime factors of 10224 and 10240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10224 and 10240.

How to find the GCF of 10224 and 10240?

We will first find the prime factorization of 10224 and 10240. After we will calculate the factors of 10224 and 10240 and find the biggest common factor number .

Step-1: Prime Factorization of 10224

Prime factors of 10224 are 2, 3, 71. Prime factorization of 10224 in exponential form is:

10224 = 2⁴ × 3² × 71¹

Step-2: Prime Factorization of 10240

Prime factors of 10240 are 2, 5. Prime factorization of 10240 in exponential form is:

10240 = 2¹¹ × 5¹

Step-3: Factors of 10224

List of positive integer factors of 10224 that divides 10224 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 71, 72, 142, 144, 213, 284, 426, 568, 639, 852, 1136, 1278, 1704, 2556, 3408, 5112

Step-4: Factors of 10240

List of positive integer factors of 10240 that divides 10224 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048, 2560, 5120

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10224 and 10240. The biggest common factor number is the GCF number.
So the greatest common factor 10224 and 10240 is 16.

Also check out the Least Common Multiple of 10224 and 10240