What is the Greatest Common Factor of 10724 and 10738?

Greatest common factor (GCF) of 10724 and 10738 is 14.

GCF(10724,10738) = 14

We will now calculate the prime factors of 10724 and 10738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10724 and 10738.

How to find the GCF of 10724 and 10738?

We will first find the prime factorization of 10724 and 10738. After we will calculate the factors of 10724 and 10738 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10738

Prime factors of 10738 are 2, 7, 13, 59. Prime factorization of 10738 in exponential form is:

10738 = 2¹ × 7¹ × 13¹ × 59¹

Step-3: Factors of 10724

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

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

Step-4: Factors of 10738

List of positive integer factors of 10738 that divides 10724 without a remainder.

1, 2, 7, 13, 14, 26, 59, 91, 118, 182, 413, 767, 826, 1534, 5369

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10724 and 10738. The biggest common factor number is the GCF number.
So the greatest common factor 10724 and 10738 is 14.

Also check out the Least Common Multiple of 10724 and 10738