What is the Greatest Common Factor of 10374 and 10380?

Greatest common factor (GCF) of 10374 and 10380 is 6.

GCF(10374,10380) = 6

We will now calculate the prime factors of 10374 and 10380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10374 and 10380.

How to find the GCF of 10374 and 10380?

We will first find the prime factorization of 10374 and 10380. After we will calculate the factors of 10374 and 10380 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 10380

Prime factors of 10380 are 2, 3, 5, 173. Prime factorization of 10380 in exponential form is:

10380 = 2² × 3¹ × 5¹ × 173¹

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 10380

List of positive integer factors of 10380 that divides 10374 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 173, 346, 519, 692, 865, 1038, 1730, 2076, 2595, 3460, 5190

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10374 and 10380. The biggest common factor number is the GCF number.
So the greatest common factor 10374 and 10380 is 6.

Also check out the Least Common Multiple of 10374 and 10380