What is the Greatest Common Factor of 10500 and 10507?

Greatest common factor (GCF) of 10500 and 10507 is 7.

GCF(10500,10507) = 7

We will now calculate the prime factors of 10500 and 10507, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10500 and 10507.

How to find the GCF of 10500 and 10507?

We will first find the prime factorization of 10500 and 10507. After we will calculate the factors of 10500 and 10507 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 10507

Prime factors of 10507 are 7, 19, 79. Prime factorization of 10507 in exponential form is:

10507 = 7¹ × 19¹ × 79¹

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 10507

List of positive integer factors of 10507 that divides 10500 without a remainder.

1, 7, 19, 79, 133, 553, 1501

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10500 and 10507. The biggest common factor number is the GCF number.
So the greatest common factor 10500 and 10507 is 7.

Also check out the Least Common Multiple of 10500 and 10507