What is the Greatest Common Factor of 84075 and 84084?

Greatest common factor (GCF) of 84075 and 84084 is 3.

GCF(84075,84084) = 3

We will now calculate the prime factors of 84075 and 84084, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84075 and 84084.

How to find the GCF of 84075 and 84084?

We will first find the prime factorization of 84075 and 84084. After we will calculate the factors of 84075 and 84084 and find the biggest common factor number .

Step-1: Prime Factorization of 84075

Prime factors of 84075 are 3, 5, 19, 59. Prime factorization of 84075 in exponential form is:

84075 = 3¹ × 5² × 19¹ × 59¹

Step-2: Prime Factorization of 84084

Prime factors of 84084 are 2, 3, 7, 11, 13. Prime factorization of 84084 in exponential form is:

84084 = 2² × 3¹ × 7² × 11¹ × 13¹

Step-3: Factors of 84075

List of positive integer factors of 84075 that divides 84075 without a remainder.

1, 3, 5, 15, 19, 25, 57, 59, 75, 95, 177, 285, 295, 475, 885, 1121, 1425, 1475, 3363, 4425, 5605, 16815, 28025

Step-4: Factors of 84084

List of positive integer factors of 84084 that divides 84075 without a remainder.

1, 2, 3, 4, 6, 7, 11, 12, 13, 14, 21, 22, 26, 28, 33, 39, 42, 44, 49, 52, 66, 77, 78, 84, 91, 98, 132, 143, 147, 154, 156, 182, 196, 231, 273, 286, 294, 308, 364, 429, 462, 539, 546, 572, 588, 637, 858, 924, 1001, 1078, 1092, 1274, 1617, 1716, 1911, 2002, 2156, 2548, 3003, 3234, 3822, 4004, 6006, 6468, 7007, 7644, 12012, 14014, 21021, 28028, 42042

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84075 and 84084. The biggest common factor number is the GCF number.
So the greatest common factor 84075 and 84084 is 3.

Also check out the Least Common Multiple of 84075 and 84084