What is the Greatest Common Factor of 43664 and 43680?

Greatest common factor (GCF) of 43664 and 43680 is 16.

GCF(43664,43680) = 16

We will now calculate the prime factors of 43664 and 43680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43664 and 43680.

How to find the GCF of 43664 and 43680?

We will first find the prime factorization of 43664 and 43680. After we will calculate the factors of 43664 and 43680 and find the biggest common factor number .

Step-1: Prime Factorization of 43664

Prime factors of 43664 are 2, 2729. Prime factorization of 43664 in exponential form is:

43664 = 2⁴ × 2729¹

Step-2: Prime Factorization of 43680

Prime factors of 43680 are 2, 3, 5, 7, 13. Prime factorization of 43680 in exponential form is:

43680 = 2⁵ × 3¹ × 5¹ × 7¹ × 13¹

Step-3: Factors of 43664

List of positive integer factors of 43664 that divides 43664 without a remainder.

1, 2, 4, 8, 16, 2729, 5458, 10916, 21832

Step-4: Factors of 43680

List of positive integer factors of 43680 that divides 43664 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 20, 21, 24, 26, 28, 30, 32, 35, 39, 40, 42, 48, 52, 56, 60, 65, 70, 78, 80, 84, 91, 96, 104, 105, 112, 120, 130, 140, 156, 160, 168, 182, 195, 208, 210, 224, 240, 260, 273, 280, 312, 336, 364, 390, 416, 420, 455, 480, 520, 546, 560, 624, 672, 728, 780, 840, 910, 1040, 1092, 1120, 1248, 1365, 1456, 1560, 1680, 1820, 2080, 2184, 2730, 2912, 3120, 3360, 3640, 4368, 5460, 6240, 7280, 8736, 10920, 14560, 21840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43664 and 43680. The biggest common factor number is the GCF number.
So the greatest common factor 43664 and 43680 is 16.

Also check out the Least Common Multiple of 43664 and 43680