What is the Greatest Common Factor of 84584 and 84600?

Greatest common factor (GCF) of 84584 and 84600 is 8.

GCF(84584,84600) = 8

We will now calculate the prime factors of 84584 and 84600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84584 and 84600.

How to find the GCF of 84584 and 84600?

We will first find the prime factorization of 84584 and 84600. After we will calculate the factors of 84584 and 84600 and find the biggest common factor number .

Step-1: Prime Factorization of 84584

Prime factors of 84584 are 2, 97, 109. Prime factorization of 84584 in exponential form is:

84584 = 2³ × 97¹ × 109¹

Step-2: Prime Factorization of 84600

Prime factors of 84600 are 2, 3, 5, 47. Prime factorization of 84600 in exponential form is:

84600 = 2³ × 3² × 5² × 47¹

Step-3: Factors of 84584

List of positive integer factors of 84584 that divides 84584 without a remainder.

1, 2, 4, 8, 97, 109, 194, 218, 388, 436, 776, 872, 10573, 21146, 42292

Step-4: Factors of 84600

List of positive integer factors of 84600 that divides 84584 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 47, 50, 60, 72, 75, 90, 94, 100, 120, 141, 150, 180, 188, 200, 225, 235, 282, 300, 360, 376, 423, 450, 470, 564, 600, 705, 846, 900, 940, 1128, 1175, 1410, 1692, 1800, 1880, 2115, 2350, 2820, 3384, 3525, 4230, 4700, 5640, 7050, 8460, 9400, 10575, 14100, 16920, 21150, 28200, 42300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84584 and 84600. The biggest common factor number is the GCF number.
So the greatest common factor 84584 and 84600 is 8.

Also check out the Least Common Multiple of 84584 and 84600