What is the Greatest Common Factor of 10416 and 10430?

Greatest common factor (GCF) of 10416 and 10430 is 14.

GCF(10416,10430) = 14

We will now calculate the prime factors of 10416 and 10430, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10416 and 10430.

How to find the GCF of 10416 and 10430?

We will first find the prime factorization of 10416 and 10430. After we will calculate the factors of 10416 and 10430 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10430

Prime factors of 10430 are 2, 5, 7, 149. Prime factorization of 10430 in exponential form is:

10430 = 2¹ × 5¹ × 7¹ × 149¹

Step-3: Factors of 10416

List of positive integer factors of 10416 that divides 10416 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

Step-4: Factors of 10430

List of positive integer factors of 10430 that divides 10416 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 149, 298, 745, 1043, 1490, 2086, 5215

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10416 and 10430. The biggest common factor number is the GCF number.
So the greatest common factor 10416 and 10430 is 14.

Also check out the Least Common Multiple of 10416 and 10430