What is the Greatest Common Factor of 10500 and 10506?

Greatest common factor (GCF) of 10500 and 10506 is 6.

GCF(10500,10506) = 6

We will now calculate the prime factors of 10500 and 10506, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10500 and 10506.

How to find the GCF of 10500 and 10506?

We will first find the prime factorization of 10500 and 10506. After we will calculate the factors of 10500 and 10506 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 10506

Prime factors of 10506 are 2, 3, 17, 103. Prime factorization of 10506 in exponential form is:

10506 = 2¹ × 3¹ × 17¹ × 103¹

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 10506

List of positive integer factors of 10506 that divides 10500 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 103, 206, 309, 618, 1751, 3502, 5253

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10500 and 10506. The biggest common factor number is the GCF number.
So the greatest common factor 10500 and 10506 is 6.

Also check out the Least Common Multiple of 10500 and 10506