What is the Greatest Common Factor of 10290 and 10304?

Greatest common factor (GCF) of 10290 and 10304 is 14.

GCF(10290,10304) = 14

We will now calculate the prime factors of 10290 and 10304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10290 and 10304.

How to find the GCF of 10290 and 10304?

We will first find the prime factorization of 10290 and 10304. After we will calculate the factors of 10290 and 10304 and find the biggest common factor number .

Step-1: Prime Factorization of 10290

Prime factors of 10290 are 2, 3, 5, 7. Prime factorization of 10290 in exponential form is:

10290 = 2¹ × 3¹ × 5¹ × 7³

Step-2: Prime Factorization of 10304

Prime factors of 10304 are 2, 7, 23. Prime factorization of 10304 in exponential form is:

10304 = 2⁶ × 7¹ × 23¹

Step-3: Factors of 10290

List of positive integer factors of 10290 that divides 10290 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 343, 490, 686, 735, 1029, 1470, 1715, 2058, 3430, 5145

Step-4: Factors of 10304

List of positive integer factors of 10304 that divides 10290 without a remainder.

1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 56, 64, 92, 112, 161, 184, 224, 322, 368, 448, 644, 736, 1288, 1472, 2576, 5152

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10290 and 10304. The biggest common factor number is the GCF number.
So the greatest common factor 10290 and 10304 is 14.

Also check out the Least Common Multiple of 10290 and 10304