What is the Greatest Common Factor of 51888 and 51900?

Greatest common factor (GCF) of 51888 and 51900 is 12.

GCF(51888,51900) = 12

We will now calculate the prime factors of 51888 and 51900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51888 and 51900.

How to find the GCF of 51888 and 51900?

We will first find the prime factorization of 51888 and 51900. After we will calculate the factors of 51888 and 51900 and find the biggest common factor number .

Step-1: Prime Factorization of 51888

Prime factors of 51888 are 2, 3, 23, 47. Prime factorization of 51888 in exponential form is:

51888 = 2⁴ × 3¹ × 23¹ × 47¹

Step-2: Prime Factorization of 51900

Prime factors of 51900 are 2, 3, 5, 173. Prime factorization of 51900 in exponential form is:

51900 = 2² × 3¹ × 5² × 173¹

Step-3: Factors of 51888

List of positive integer factors of 51888 that divides 51888 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 46, 47, 48, 69, 92, 94, 138, 141, 184, 188, 276, 282, 368, 376, 552, 564, 752, 1081, 1104, 1128, 2162, 2256, 3243, 4324, 6486, 8648, 12972, 17296, 25944

Step-4: Factors of 51900

List of positive integer factors of 51900 that divides 51888 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 173, 300, 346, 519, 692, 865, 1038, 1730, 2076, 2595, 3460, 4325, 5190, 8650, 10380, 12975, 17300, 25950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51888 and 51900. The biggest common factor number is the GCF number.
So the greatest common factor 51888 and 51900 is 12.

Also check out the Least Common Multiple of 51888 and 51900