What is the Greatest Common Factor of 84144 and 84164?

Greatest common factor (GCF) of 84144 and 84164 is 4.

GCF(84144,84164) = 4

We will now calculate the prime factors of 84144 and 84164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84144 and 84164.

How to find the GCF of 84144 and 84164?

We will first find the prime factorization of 84144 and 84164. After we will calculate the factors of 84144 and 84164 and find the biggest common factor number .

Step-1: Prime Factorization of 84144

Prime factors of 84144 are 2, 3, 1753. Prime factorization of 84144 in exponential form is:

84144 = 2⁴ × 3¹ × 1753¹

Step-2: Prime Factorization of 84164

Prime factors of 84164 are 2, 53, 397. Prime factorization of 84164 in exponential form is:

84164 = 2² × 53¹ × 397¹

Step-3: Factors of 84144

List of positive integer factors of 84144 that divides 84144 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1753, 3506, 5259, 7012, 10518, 14024, 21036, 28048, 42072

Step-4: Factors of 84164

List of positive integer factors of 84164 that divides 84144 without a remainder.

1, 2, 4, 53, 106, 212, 397, 794, 1588, 21041, 42082

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84144 and 84164. The biggest common factor number is the GCF number.
So the greatest common factor 84144 and 84164 is 4.

Also check out the Least Common Multiple of 84144 and 84164