What is the Greatest Common Factor of 24500 and 24514?

Greatest common factor (GCF) of 24500 and 24514 is 14.

GCF(24500,24514) = 14

We will now calculate the prime factors of 24500 and 24514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 24500 and 24514.

How to find the GCF of 24500 and 24514?

We will first find the prime factorization of 24500 and 24514. After we will calculate the factors of 24500 and 24514 and find the biggest common factor number .

Step-1: Prime Factorization of 24500

Prime factors of 24500 are 2, 5, 7. Prime factorization of 24500 in exponential form is:

24500 = 2² × 5³ × 7²

Step-2: Prime Factorization of 24514

Prime factors of 24514 are 2, 7, 17, 103. Prime factorization of 24514 in exponential form is:

24514 = 2¹ × 7¹ × 17¹ × 103¹

Step-3: Factors of 24500

List of positive integer factors of 24500 that divides 24500 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 125, 140, 175, 196, 245, 250, 350, 490, 500, 700, 875, 980, 1225, 1750, 2450, 3500, 4900, 6125, 12250

Step-4: Factors of 24514

List of positive integer factors of 24514 that divides 24500 without a remainder.

1, 2, 7, 14, 17, 34, 103, 119, 206, 238, 721, 1442, 1751, 3502, 12257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 24500 and 24514. The biggest common factor number is the GCF number.
So the greatest common factor 24500 and 24514 is 14.

Also check out the Least Common Multiple of 24500 and 24514