What is the Greatest Common Factor of 2240 and 2254?

Greatest common factor (GCF) of 2240 and 2254 is 14.

GCF(2240,2254) = 14

We will now calculate the prime factors of 2240 and 2254, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2240 and 2254.

How to find the GCF of 2240 and 2254?

We will first find the prime factorization of 2240 and 2254. After we will calculate the factors of 2240 and 2254 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 2254

Prime factors of 2254 are 2, 7, 23. Prime factorization of 2254 in exponential form is:

2254 = 2¹ × 7² × 23¹

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 2254

List of positive integer factors of 2254 that divides 2240 without a remainder.

1, 2, 7, 14, 23, 46, 49, 98, 161, 322, 1127

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2240 and 2254. The biggest common factor number is the GCF number.
So the greatest common factor 2240 and 2254 is 14.

Also check out the Least Common Multiple of 2240 and 2254