What is the Greatest Common Factor of 10374 and 10388?

Greatest common factor (GCF) of 10374 and 10388 is 14.

GCF(10374,10388) = 14

We will now calculate the prime factors of 10374 and 10388, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10374 and 10388.

How to find the GCF of 10374 and 10388?

We will first find the prime factorization of 10374 and 10388. After we will calculate the factors of 10374 and 10388 and find the biggest common factor number .

Step-1: Prime Factorization of 10374

Prime factors of 10374 are 2, 3, 7, 13, 19. Prime factorization of 10374 in exponential form is:

10374 = 2¹ × 3¹ × 7¹ × 13¹ × 19¹

Step-2: Prime Factorization of 10388

Prime factors of 10388 are 2, 7, 53. Prime factorization of 10388 in exponential form is:

10388 = 2² × 7² × 53¹

Step-3: Factors of 10374

List of positive integer factors of 10374 that divides 10374 without a remainder.

1, 2, 3, 6, 7, 13, 14, 19, 21, 26, 38, 39, 42, 57, 78, 91, 114, 133, 182, 247, 266, 273, 399, 494, 546, 741, 798, 1482, 1729, 3458, 5187

Step-4: Factors of 10388

List of positive integer factors of 10388 that divides 10374 without a remainder.

1, 2, 4, 7, 14, 28, 49, 53, 98, 106, 196, 212, 371, 742, 1484, 2597, 5194

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10374 and 10388. The biggest common factor number is the GCF number.
So the greatest common factor 10374 and 10388 is 14.

Also check out the Least Common Multiple of 10374 and 10388