What is the Greatest Common Factor of 45888 and 45900?

Greatest common factor (GCF) of 45888 and 45900 is 12.

GCF(45888,45900) = 12

We will now calculate the prime factors of 45888 and 45900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45888 and 45900.

How to find the GCF of 45888 and 45900?

We will first find the prime factorization of 45888 and 45900. After we will calculate the factors of 45888 and 45900 and find the biggest common factor number .

Step-1: Prime Factorization of 45888

Prime factors of 45888 are 2, 3, 239. Prime factorization of 45888 in exponential form is:

45888 = 2⁶ × 3¹ × 239¹

Step-2: Prime Factorization of 45900

Prime factors of 45900 are 2, 3, 5, 17. Prime factorization of 45900 in exponential form is:

45900 = 2² × 3³ × 5² × 17¹

Step-3: Factors of 45888

List of positive integer factors of 45888 that divides 45888 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 239, 478, 717, 956, 1434, 1912, 2868, 3824, 5736, 7648, 11472, 15296, 22944

Step-4: Factors of 45900

List of positive integer factors of 45900 that divides 45888 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 25, 27, 30, 34, 36, 45, 50, 51, 54, 60, 68, 75, 85, 90, 100, 102, 108, 135, 150, 153, 170, 180, 204, 225, 255, 270, 300, 306, 340, 425, 450, 459, 510, 540, 612, 675, 765, 850, 900, 918, 1020, 1275, 1350, 1530, 1700, 1836, 2295, 2550, 2700, 3060, 3825, 4590, 5100, 7650, 9180, 11475, 15300, 22950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45888 and 45900. The biggest common factor number is the GCF number.
So the greatest common factor 45888 and 45900 is 12.

Also check out the Least Common Multiple of 45888 and 45900