What is the Greatest Common Factor of 43680 and 43694?

Greatest common factor (GCF) of 43680 and 43694 is 14.

GCF(43680,43694) = 14

We will now calculate the prime factors of 43680 and 43694, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43680 and 43694.

How to find the GCF of 43680 and 43694?

We will first find the prime factorization of 43680 and 43694. After we will calculate the factors of 43680 and 43694 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 43694

Prime factors of 43694 are 2, 7, 3121. Prime factorization of 43694 in exponential form is:

43694 = 2¹ × 7¹ × 3121¹

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 43694

List of positive integer factors of 43694 that divides 43680 without a remainder.

1, 2, 7, 14, 3121, 6242, 21847

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43680 and 43694. The biggest common factor number is the GCF number.
So the greatest common factor 43680 and 43694 is 14.

Also check out the Least Common Multiple of 43680 and 43694