What is the Greatest Common Factor of 2256 and 2265?

Greatest common factor (GCF) of 2256 and 2265 is 3.

GCF(2256,2265) = 3

We will now calculate the prime factors of 2256 and 2265, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2256 and 2265.

How to find the GCF of 2256 and 2265?

We will first find the prime factorization of 2256 and 2265. After we will calculate the factors of 2256 and 2265 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 2265

Prime factors of 2265 are 3, 5, 151. Prime factorization of 2265 in exponential form is:

2265 = 3¹ × 5¹ × 151¹

Step-3: Factors of 2256

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

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

Step-4: Factors of 2265

List of positive integer factors of 2265 that divides 2256 without a remainder.

1, 3, 5, 15, 151, 453, 755

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2256 and 2265. The biggest common factor number is the GCF number.
So the greatest common factor 2256 and 2265 is 3.

Also check out the Least Common Multiple of 2256 and 2265