What is the Greatest Common Factor of 51870 and 51888?

Greatest common factor (GCF) of 51870 and 51888 is 6.

GCF(51870,51888) = 6

We will now calculate the prime factors of 51870 and 51888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51870 and 51888.

How to find the GCF of 51870 and 51888?

We will first find the prime factorization of 51870 and 51888. After we will calculate the factors of 51870 and 51888 and find the biggest common factor number .

Step-1: Prime Factorization of 51870

Prime factors of 51870 are 2, 3, 5, 7, 13, 19. Prime factorization of 51870 in exponential form is:

51870 = 2¹ × 3¹ × 5¹ × 7¹ × 13¹ × 19¹

Step-2: 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-3: Factors of 51870

List of positive integer factors of 51870 that divides 51870 without a remainder.

1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 19, 21, 26, 30, 35, 38, 39, 42, 57, 65, 70, 78, 91, 95, 105, 114, 130, 133, 182, 190, 195, 210, 247, 266, 273, 285, 390, 399, 455, 494, 546, 570, 665, 741, 798, 910, 1235, 1330, 1365, 1482, 1729, 1995, 2470, 2730, 3458, 3705, 3990, 5187, 7410, 8645, 10374, 17290, 25935

Step-4: Factors of 51888

List of positive integer factors of 51888 that divides 51870 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51870 and 51888. The biggest common factor number is the GCF number.
So the greatest common factor 51870 and 51888 is 6.

Also check out the Least Common Multiple of 51870 and 51888