What is the Greatest Common Factor of 15296 and 15300?

Greatest common factor (GCF) of 15296 and 15300 is 4.

GCF(15296,15300) = 4

We will now calculate the prime factors of 15296 and 15300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15296 and 15300.

How to find the GCF of 15296 and 15300?

We will first find the prime factorization of 15296 and 15300. After we will calculate the factors of 15296 and 15300 and find the biggest common factor number .

Step-1: Prime Factorization of 15296

Prime factors of 15296 are 2, 239. Prime factorization of 15296 in exponential form is:

15296 = 2⁶ × 239¹

Step-2: Prime Factorization of 15300

Prime factors of 15300 are 2, 3, 5, 17. Prime factorization of 15300 in exponential form is:

15300 = 2² × 3² × 5² × 17¹

Step-3: Factors of 15296

List of positive integer factors of 15296 that divides 15296 without a remainder.

1, 2, 4, 8, 16, 32, 64, 239, 478, 956, 1912, 3824, 7648

Step-4: Factors of 15300

List of positive integer factors of 15300 that divides 15296 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 25, 30, 34, 36, 45, 50, 51, 60, 68, 75, 85, 90, 100, 102, 150, 153, 170, 180, 204, 225, 255, 300, 306, 340, 425, 450, 510, 612, 765, 850, 900, 1020, 1275, 1530, 1700, 2550, 3060, 3825, 5100, 7650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15296 and 15300. The biggest common factor number is the GCF number.
So the greatest common factor 15296 and 15300 is 4.

Also check out the Least Common Multiple of 15296 and 15300