What is the Greatest Common Factor of 2233 and 2240?

Greatest common factor (GCF) of 2233 and 2240 is 7.

GCF(2233,2240) = 7

We will now calculate the prime factors of 2233 and 2240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2233 and 2240.

How to find the GCF of 2233 and 2240?

We will first find the prime factorization of 2233 and 2240. After we will calculate the factors of 2233 and 2240 and find the biggest common factor number .

Step-1: Prime Factorization of 2233

Prime factors of 2233 are 7, 11, 29. Prime factorization of 2233 in exponential form is:

2233 = 7¹ × 11¹ × 29¹

Step-2: 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-3: Factors of 2233

List of positive integer factors of 2233 that divides 2233 without a remainder.

1, 7, 11, 29, 77, 203, 319

Step-4: Factors of 2240

List of positive integer factors of 2240 that divides 2233 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2233 and 2240. The biggest common factor number is the GCF number.
So the greatest common factor 2233 and 2240 is 7.

Also check out the Least Common Multiple of 2233 and 2240