What is the Greatest Common Factor of 43680 and 43696?

Greatest common factor (GCF) of 43680 and 43696 is 16.

GCF(43680,43696) = 16

We will now calculate the prime factors of 43680 and 43696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43680 and 43696.

How to find the GCF of 43680 and 43696?

We will first find the prime factorization of 43680 and 43696. After we will calculate the factors of 43680 and 43696 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 43696

Prime factors of 43696 are 2, 2731. Prime factorization of 43696 in exponential form is:

43696 = 2⁴ × 2731¹

Step-3: Factors of 43680

List of positive integer factors of 43680 that divides 43680 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

Step-4: Factors of 43696

List of positive integer factors of 43696 that divides 43680 without a remainder.

1, 2, 4, 8, 16, 2731, 5462, 10924, 21848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43680 and 43696. The biggest common factor number is the GCF number.
So the greatest common factor 43680 and 43696 is 16.

Also check out the Least Common Multiple of 43680 and 43696