What is the Greatest Common Factor of 10738 and 10745?

Greatest common factor (GCF) of 10738 and 10745 is 7.

GCF(10738,10745) = 7

We will now calculate the prime factors of 10738 and 10745, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10738 and 10745.

How to find the GCF of 10738 and 10745?

We will first find the prime factorization of 10738 and 10745. After we will calculate the factors of 10738 and 10745 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10745

Prime factors of 10745 are 5, 7, 307. Prime factorization of 10745 in exponential form is:

10745 = 5¹ × 7¹ × 307¹

Step-3: Factors of 10738

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

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

Step-4: Factors of 10745

List of positive integer factors of 10745 that divides 10738 without a remainder.

1, 5, 7, 35, 307, 1535, 2149

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10738 and 10745. The biggest common factor number is the GCF number.
So the greatest common factor 10738 and 10745 is 7.

Also check out the Least Common Multiple of 10738 and 10745