What is the Greatest Common Factor of 10710 and 10724?

Greatest common factor (GCF) of 10710 and 10724 is 14.

GCF(10710,10724) = 14

We will now calculate the prime factors of 10710 and 10724, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10710 and 10724.

How to find the GCF of 10710 and 10724?

We will first find the prime factorization of 10710 and 10724. After we will calculate the factors of 10710 and 10724 and find the biggest common factor number .

Step-1: Prime Factorization of 10710

Prime factors of 10710 are 2, 3, 5, 7, 17. Prime factorization of 10710 in exponential form is:

10710 = 2¹ × 3² × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 10724

Prime factors of 10724 are 2, 7, 383. Prime factorization of 10724 in exponential form is:

10724 = 2² × 7¹ × 383¹

Step-3: Factors of 10710

List of positive integer factors of 10710 that divides 10710 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 17, 18, 21, 30, 34, 35, 42, 45, 51, 63, 70, 85, 90, 102, 105, 119, 126, 153, 170, 210, 238, 255, 306, 315, 357, 510, 595, 630, 714, 765, 1071, 1190, 1530, 1785, 2142, 3570, 5355

Step-4: Factors of 10724

List of positive integer factors of 10724 that divides 10710 without a remainder.

1, 2, 4, 7, 14, 28, 383, 766, 1532, 2681, 5362

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10710 and 10724. The biggest common factor number is the GCF number.
So the greatest common factor 10710 and 10724 is 14.

Also check out the Least Common Multiple of 10710 and 10724