What is the Greatest Common Factor of 10500 and 10512?

Greatest common factor (GCF) of 10500 and 10512 is 12.

GCF(10500,10512) = 12

We will now calculate the prime factors of 10500 and 10512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10500 and 10512.

How to find the GCF of 10500 and 10512?

We will first find the prime factorization of 10500 and 10512. After we will calculate the factors of 10500 and 10512 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 10512

Prime factors of 10512 are 2, 3, 73. Prime factorization of 10512 in exponential form is:

10512 = 2⁴ × 3² × 73¹

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 10512

List of positive integer factors of 10512 that divides 10500 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 73, 144, 146, 219, 292, 438, 584, 657, 876, 1168, 1314, 1752, 2628, 3504, 5256

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10500 and 10512. The biggest common factor number is the GCF number.
So the greatest common factor 10500 and 10512 is 12.

Also check out the Least Common Multiple of 10500 and 10512