What is the Greatest Common Factor of 10500 and 10520?

Greatest common factor (GCF) of 10500 and 10520 is 20.

GCF(10500,10520) = 20

We will now calculate the prime factors of 10500 and 10520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10500 and 10520.

How to find the GCF of 10500 and 10520?

We will first find the prime factorization of 10500 and 10520. After we will calculate the factors of 10500 and 10520 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 10520

Prime factors of 10520 are 2, 5, 263. Prime factorization of 10520 in exponential form is:

10520 = 2³ × 5¹ × 263¹

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 10520

List of positive integer factors of 10520 that divides 10500 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 263, 526, 1052, 1315, 2104, 2630, 5260

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10500 and 10520. The biggest common factor number is the GCF number.
So the greatest common factor 10500 and 10520 is 20.

Also check out the Least Common Multiple of 10500 and 10520