What is the Greatest Common Factor of 53854 and 53872?

Greatest common factor (GCF) of 53854 and 53872 is 2.

GCF(53854,53872) = 2

We will now calculate the prime factors of 53854 and 53872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53854 and 53872.

How to find the GCF of 53854 and 53872?

We will first find the prime factorization of 53854 and 53872. After we will calculate the factors of 53854 and 53872 and find the biggest common factor number .

Step-1: Prime Factorization of 53854

Prime factors of 53854 are 2, 26927. Prime factorization of 53854 in exponential form is:

53854 = 2¹ × 26927¹

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 53854

List of positive integer factors of 53854 that divides 53854 without a remainder.

1, 2, 26927

Step-4: Factors of 53872

List of positive integer factors of 53872 that divides 53854 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 53854 and 53872. The biggest common factor number is the GCF number.
So the greatest common factor 53854 and 53872 is 2.

Also check out the Least Common Multiple of 53854 and 53872