What is the Greatest Common Factor of 2240 and 2258?

Greatest common factor (GCF) of 2240 and 2258 is 2.

GCF(2240,2258) = 2

We will now calculate the prime factors of 2240 and 2258, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2240 and 2258.

How to find the GCF of 2240 and 2258?

We will first find the prime factorization of 2240 and 2258. After we will calculate the factors of 2240 and 2258 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 2258

Prime factors of 2258 are 2, 1129. Prime factorization of 2258 in exponential form is:

2258 = 2¹ × 1129¹

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 2258

List of positive integer factors of 2258 that divides 2240 without a remainder.

1, 2, 1129

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2240 and 2258. The biggest common factor number is the GCF number.
So the greatest common factor 2240 and 2258 is 2.

Also check out the Least Common Multiple of 2240 and 2258