What is the Greatest Common Factor of 10480 and 10500?

Greatest common factor (GCF) of 10480 and 10500 is 20.

GCF(10480,10500) = 20

We will now calculate the prime factors of 10480 and 10500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10480 and 10500.

How to find the GCF of 10480 and 10500?

We will first find the prime factorization of 10480 and 10500. After we will calculate the factors of 10480 and 10500 and find the biggest common factor number .

Step-1: Prime Factorization of 10480

Prime factors of 10480 are 2, 5, 131. Prime factorization of 10480 in exponential form is:

10480 = 2⁴ × 5¹ × 131¹

Step-2: 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-3: Factors of 10480

List of positive integer factors of 10480 that divides 10480 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 131, 262, 524, 655, 1048, 1310, 2096, 2620, 5240

Step-4: Factors of 10500

List of positive integer factors of 10500 that divides 10480 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10480 and 10500. The biggest common factor number is the GCF number.
So the greatest common factor 10480 and 10500 is 20.

Also check out the Least Common Multiple of 10480 and 10500