What is the Greatest Common Factor of 53856 and 53872?

Greatest common factor (GCF) of 53856 and 53872 is 16.

GCF(53856,53872) = 16

We will now calculate the prime factors of 53856 and 53872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53856 and 53872.

How to find the GCF of 53856 and 53872?

We will first find the prime factorization of 53856 and 53872. After we will calculate the factors of 53856 and 53872 and find the biggest common factor number .

Step-1: Prime Factorization of 53856

Prime factors of 53856 are 2, 3, 11, 17. Prime factorization of 53856 in exponential form is:

53856 = 2⁵ × 3² × 11¹ × 17¹

Step-2: Prime Factorization of 53872

Prime factors of 53872 are 2, 7, 13, 37. Prime factorization of 53872 in exponential form is:

53872 = 2⁴ × 7¹ × 13¹ × 37¹

Step-3: Factors of 53856

List of positive integer factors of 53856 that divides 53856 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 17, 18, 22, 24, 32, 33, 34, 36, 44, 48, 51, 66, 68, 72, 88, 96, 99, 102, 132, 136, 144, 153, 176, 187, 198, 204, 264, 272, 288, 306, 352, 374, 396, 408, 528, 544, 561, 612, 748, 792, 816, 1056, 1122, 1224, 1496, 1584, 1632, 1683, 2244, 2448, 2992, 3168, 3366, 4488, 4896, 5984, 6732, 8976, 13464, 17952, 26928

Step-4: Factors of 53872

List of positive integer factors of 53872 that divides 53856 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 37, 52, 56, 74, 91, 104, 112, 148, 182, 208, 259, 296, 364, 481, 518, 592, 728, 962, 1036, 1456, 1924, 2072, 3367, 3848, 4144, 6734, 7696, 13468, 26936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53856 and 53872. The biggest common factor number is the GCF number.
So the greatest common factor 53856 and 53872 is 16.

Also check out the Least Common Multiple of 53856 and 53872