What is the Greatest Common Factor of 2240 and 2256?

Greatest common factor (GCF) of 2240 and 2256 is 16.

GCF(2240,2256) = 16

We will now calculate the prime factors of 2240 and 2256, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2240 and 2256.

How to find the GCF of 2240 and 2256?

We will first find the prime factorization of 2240 and 2256. After we will calculate the factors of 2240 and 2256 and find the biggest common factor number .

Step-1: Prime Factorization of 2240

Prime factors of 2240 are 2, 5, 7. Prime factorization of 2240 in exponential form is:

2240 = 2⁶ × 5¹ × 7¹

Step-2: Prime Factorization of 2256

Prime factors of 2256 are 2, 3, 47. Prime factorization of 2256 in exponential form is:

2256 = 2⁴ × 3¹ × 47¹

Step-3: Factors of 2240

List of positive integer factors of 2240 that divides 2240 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120

Step-4: Factors of 2256

List of positive integer factors of 2256 that divides 2240 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 47, 48, 94, 141, 188, 282, 376, 564, 752, 1128

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2240 and 2256. The biggest common factor number is the GCF number.
So the greatest common factor 2240 and 2256 is 16.

Also check out the Least Common Multiple of 2240 and 2256