What is the Greatest Common Factor of 10380 and 10400?

Greatest common factor (GCF) of 10380 and 10400 is 20.

GCF(10380,10400) = 20

We will now calculate the prime factors of 10380 and 10400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10380 and 10400.

How to find the GCF of 10380 and 10400?

We will first find the prime factorization of 10380 and 10400. After we will calculate the factors of 10380 and 10400 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10400

Prime factors of 10400 are 2, 5, 13. Prime factorization of 10400 in exponential form is:

10400 = 2⁵ × 5² × 13¹

Step-3: Factors of 10380

List of positive integer factors of 10380 that divides 10380 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

Step-4: Factors of 10400

List of positive integer factors of 10400 that divides 10380 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10380 and 10400. The biggest common factor number is the GCF number.
So the greatest common factor 10380 and 10400 is 20.

Also check out the Least Common Multiple of 10380 and 10400