What is the Greatest Common Factor of 16875 and 16884?

Greatest common factor (GCF) of 16875 and 16884 is 9.

GCF(16875,16884) = 9

We will now calculate the prime factors of 16875 and 16884, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16875 and 16884.

How to find the GCF of 16875 and 16884?

We will first find the prime factorization of 16875 and 16884. After we will calculate the factors of 16875 and 16884 and find the biggest common factor number .

Step-1: Prime Factorization of 16875

Prime factors of 16875 are 3, 5. Prime factorization of 16875 in exponential form is:

16875 = 3³ × 5⁴

Step-2: Prime Factorization of 16884

Prime factors of 16884 are 2, 3, 7, 67. Prime factorization of 16884 in exponential form is:

16884 = 2² × 3² × 7¹ × 67¹

Step-3: Factors of 16875

List of positive integer factors of 16875 that divides 16875 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 125, 135, 225, 375, 625, 675, 1125, 1875, 3375, 5625

Step-4: Factors of 16884

List of positive integer factors of 16884 that divides 16875 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 67, 84, 126, 134, 201, 252, 268, 402, 469, 603, 804, 938, 1206, 1407, 1876, 2412, 2814, 4221, 5628, 8442

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16875 and 16884. The biggest common factor number is the GCF number.
So the greatest common factor 16875 and 16884 is 9.

Also check out the Least Common Multiple of 16875 and 16884