What is the Greatest Common Factor of 55680 and 55692?

Greatest common factor (GCF) of 55680 and 55692 is 12.

GCF(55680,55692) = 12

We will now calculate the prime factors of 55680 and 55692, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55680 and 55692.

How to find the GCF of 55680 and 55692?

We will first find the prime factorization of 55680 and 55692. After we will calculate the factors of 55680 and 55692 and find the biggest common factor number .

Step-1: Prime Factorization of 55680

Prime factors of 55680 are 2, 3, 5, 29. Prime factorization of 55680 in exponential form is:

55680 = 2⁷ × 3¹ × 5¹ × 29¹

Step-2: Prime Factorization of 55692

Prime factors of 55692 are 2, 3, 7, 13, 17. Prime factorization of 55692 in exponential form is:

55692 = 2² × 3² × 7¹ × 13¹ × 17¹

Step-3: Factors of 55680

List of positive integer factors of 55680 that divides 55680 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 29, 30, 32, 40, 48, 58, 60, 64, 80, 87, 96, 116, 120, 128, 145, 160, 174, 192, 232, 240, 290, 320, 348, 384, 435, 464, 480, 580, 640, 696, 870, 928, 960, 1160, 1392, 1740, 1856, 1920, 2320, 2784, 3480, 3712, 4640, 5568, 6960, 9280, 11136, 13920, 18560, 27840

Step-4: Factors of 55692

List of positive integer factors of 55692 that divides 55680 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 13, 14, 17, 18, 21, 26, 28, 34, 36, 39, 42, 51, 52, 63, 68, 78, 84, 91, 102, 117, 119, 126, 153, 156, 182, 204, 221, 234, 238, 252, 273, 306, 357, 364, 442, 468, 476, 546, 612, 663, 714, 819, 884, 1071, 1092, 1326, 1428, 1547, 1638, 1989, 2142, 2652, 3094, 3276, 3978, 4284, 4641, 6188, 7956, 9282, 13923, 18564, 27846

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55680 and 55692. The biggest common factor number is the GCF number.
So the greatest common factor 55680 and 55692 is 12.

Also check out the Least Common Multiple of 55680 and 55692