What is the Greatest Common Factor of 10500 and 10519?

Greatest common factor (GCF) of 10500 and 10519 is 1.

GCF(10500,10519) = 1

We will now calculate the prime factors of 10500 and 10519, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10500 and 10519.

How to find the GCF of 10500 and 10519?

We will first find the prime factorization of 10500 and 10519. After we will calculate the factors of 10500 and 10519 and find the biggest common factor number .

Step-1: Prime Factorization of 10500

Prime factors of 10500 are 2, 3, 5, 7. Prime factorization of 10500 in exponential form is:

10500 = 2² × 3¹ × 5³ × 7¹

Step-2: Prime Factorization of 10519

Prime factors of 10519 are 67, 157. Prime factorization of 10519 in exponential form is:

10519 = 67¹ × 157¹

Step-3: Factors of 10500

List of positive integer factors of 10500 that divides 10500 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 125, 140, 150, 175, 210, 250, 300, 350, 375, 420, 500, 525, 700, 750, 875, 1050, 1500, 1750, 2100, 2625, 3500, 5250

Step-4: Factors of 10519

List of positive integer factors of 10519 that divides 10500 without a remainder.

1, 67, 157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10500 and 10519. The biggest common factor number is the GCF number.
So the greatest common factor 10500 and 10519 is 1.

Also check out the Least Common Multiple of 10500 and 10519