What is the Greatest Common Factor of 10409 and 10416?

Greatest common factor (GCF) of 10409 and 10416 is 7.

GCF(10409,10416) = 7

We will now calculate the prime factors of 10409 and 10416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10409 and 10416.

How to find the GCF of 10409 and 10416?

We will first find the prime factorization of 10409 and 10416. After we will calculate the factors of 10409 and 10416 and find the biggest common factor number .

Step-1: Prime Factorization of 10409

Prime factors of 10409 are 7, 1487. Prime factorization of 10409 in exponential form is:

10409 = 7¹ × 1487¹

Step-2: Prime Factorization of 10416

Prime factors of 10416 are 2, 3, 7, 31. Prime factorization of 10416 in exponential form is:

10416 = 2⁴ × 3¹ × 7¹ × 31¹

Step-3: Factors of 10409

List of positive integer factors of 10409 that divides 10409 without a remainder.

1, 7, 1487

Step-4: Factors of 10416

List of positive integer factors of 10416 that divides 10409 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 31, 42, 48, 56, 62, 84, 93, 112, 124, 168, 186, 217, 248, 336, 372, 434, 496, 651, 744, 868, 1302, 1488, 1736, 2604, 3472, 5208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10409 and 10416. The biggest common factor number is the GCF number.
So the greatest common factor 10409 and 10416 is 7.

Also check out the Least Common Multiple of 10409 and 10416