What is the Greatest Common Factor of 10400 and 10419?

Greatest common factor (GCF) of 10400 and 10419 is 1.

GCF(10400,10419) = 1

We will now calculate the prime factors of 10400 and 10419, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10400 and 10419.

How to find the GCF of 10400 and 10419?

We will first find the prime factorization of 10400 and 10419. After we will calculate the factors of 10400 and 10419 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10419

Prime factors of 10419 are 3, 23, 151. Prime factorization of 10419 in exponential form is:

10419 = 3¹ × 23¹ × 151¹

Step-3: Factors of 10400

List of positive integer factors of 10400 that divides 10400 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

Step-4: Factors of 10419

List of positive integer factors of 10419 that divides 10400 without a remainder.

1, 3, 23, 69, 151, 453, 3473

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10400 and 10419. The biggest common factor number is the GCF number.
So the greatest common factor 10400 and 10419 is 1.

Also check out the Least Common Multiple of 10400 and 10419