What is the Greatest Common Factor of 9500 and 9514?

Greatest common factor (GCF) of 9500 and 9514 is 2.

GCF(9500,9514) = 2

We will now calculate the prime factors of 9500 and 9514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9500 and 9514.

How to find the GCF of 9500 and 9514?

We will first find the prime factorization of 9500 and 9514. After we will calculate the factors of 9500 and 9514 and find the biggest common factor number .

Step-1: Prime Factorization of 9500

Prime factors of 9500 are 2, 5, 19. Prime factorization of 9500 in exponential form is:

9500 = 2² × 5³ × 19¹

Step-2: Prime Factorization of 9514

Prime factors of 9514 are 2, 67, 71. Prime factorization of 9514 in exponential form is:

9514 = 2¹ × 67¹ × 71¹

Step-3: Factors of 9500

List of positive integer factors of 9500 that divides 9500 without a remainder.

1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 125, 190, 250, 380, 475, 500, 950, 1900, 2375, 4750

Step-4: Factors of 9514

List of positive integer factors of 9514 that divides 9500 without a remainder.

1, 2, 67, 71, 134, 142, 4757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9500 and 9514. The biggest common factor number is the GCF number.
So the greatest common factor 9500 and 9514 is 2.

Also check out the Least Common Multiple of 9500 and 9514