What is the Greatest Common Factor of 4500 and 4514?

Greatest common factor (GCF) of 4500 and 4514 is 2.

GCF(4500,4514) = 2

We will now calculate the prime factors of 4500 and 4514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4500 and 4514.

How to find the GCF of 4500 and 4514?

We will first find the prime factorization of 4500 and 4514. After we will calculate the factors of 4500 and 4514 and find the biggest common factor number .

Step-1: Prime Factorization of 4500

Prime factors of 4500 are 2, 3, 5. Prime factorization of 4500 in exponential form is:

4500 = 2² × 3² × 5³

Step-2: Prime Factorization of 4514

Prime factors of 4514 are 2, 37, 61. Prime factorization of 4514 in exponential form is:

4514 = 2¹ × 37¹ × 61¹

Step-3: Factors of 4500

List of positive integer factors of 4500 that divides 4500 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250

Step-4: Factors of 4514

List of positive integer factors of 4514 that divides 4500 without a remainder.

1, 2, 37, 61, 74, 122, 2257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4500 and 4514. The biggest common factor number is the GCF number.
So the greatest common factor 4500 and 4514 is 2.

Also check out the Least Common Multiple of 4500 and 4514