What is the Greatest Common Factor of 53648 and 53664?

Greatest common factor (GCF) of 53648 and 53664 is 16.

GCF(53648,53664) = 16

We will now calculate the prime factors of 53648 and 53664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53648 and 53664.

How to find the GCF of 53648 and 53664?

We will first find the prime factorization of 53648 and 53664. After we will calculate the factors of 53648 and 53664 and find the biggest common factor number .

Step-1: Prime Factorization of 53648

Prime factors of 53648 are 2, 7, 479. Prime factorization of 53648 in exponential form is:

53648 = 2⁴ × 7¹ × 479¹

Step-2: Prime Factorization of 53664

Prime factors of 53664 are 2, 3, 13, 43. Prime factorization of 53664 in exponential form is:

53664 = 2⁵ × 3¹ × 13¹ × 43¹

Step-3: Factors of 53648

List of positive integer factors of 53648 that divides 53648 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 479, 958, 1916, 3353, 3832, 6706, 7664, 13412, 26824

Step-4: Factors of 53664

List of positive integer factors of 53664 that divides 53648 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 43, 48, 52, 78, 86, 96, 104, 129, 156, 172, 208, 258, 312, 344, 416, 516, 559, 624, 688, 1032, 1118, 1248, 1376, 1677, 2064, 2236, 3354, 4128, 4472, 6708, 8944, 13416, 17888, 26832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53648 and 53664. The biggest common factor number is the GCF number.
So the greatest common factor 53648 and 53664 is 16.

Also check out the Least Common Multiple of 53648 and 53664