What is the Greatest Common Factor of 86784 and 86800?

Greatest common factor (GCF) of 86784 and 86800 is 16.

GCF(86784,86800) = 16

We will now calculate the prime factors of 86784 and 86800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 86784 and 86800.

How to find the GCF of 86784 and 86800?

We will first find the prime factorization of 86784 and 86800. After we will calculate the factors of 86784 and 86800 and find the biggest common factor number .

Step-1: Prime Factorization of 86784

Prime factors of 86784 are 2, 3, 113. Prime factorization of 86784 in exponential form is:

86784 = 2⁸ × 3¹ × 113¹

Step-2: Prime Factorization of 86800

Prime factors of 86800 are 2, 5, 7, 31. Prime factorization of 86800 in exponential form is:

86800 = 2⁴ × 5² × 7¹ × 31¹

Step-3: Factors of 86784

List of positive integer factors of 86784 that divides 86784 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 113, 128, 192, 226, 256, 339, 384, 452, 678, 768, 904, 1356, 1808, 2712, 3616, 5424, 7232, 10848, 14464, 21696, 28928, 43392

Step-4: Factors of 86800

List of positive integer factors of 86800 that divides 86784 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 31, 35, 40, 50, 56, 62, 70, 80, 100, 112, 124, 140, 155, 175, 200, 217, 248, 280, 310, 350, 400, 434, 496, 560, 620, 700, 775, 868, 1085, 1240, 1400, 1550, 1736, 2170, 2480, 2800, 3100, 3472, 4340, 5425, 6200, 8680, 10850, 12400, 17360, 21700, 43400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 86784 and 86800. The biggest common factor number is the GCF number.
So the greatest common factor 86784 and 86800 is 16.

Also check out the Least Common Multiple of 86784 and 86800