What is the Greatest Common Factor of 39144 and 39164?

Greatest common factor (GCF) of 39144 and 39164 is 4.

GCF(39144,39164) = 4

We will now calculate the prime factors of 39144 and 39164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39144 and 39164.

How to find the GCF of 39144 and 39164?

We will first find the prime factorization of 39144 and 39164. After we will calculate the factors of 39144 and 39164 and find the biggest common factor number .

Step-1: Prime Factorization of 39144

Prime factors of 39144 are 2, 3, 7, 233. Prime factorization of 39144 in exponential form is:

39144 = 2³ × 3¹ × 7¹ × 233¹

Step-2: Prime Factorization of 39164

Prime factors of 39164 are 2, 9791. Prime factorization of 39164 in exponential form is:

39164 = 2² × 9791¹

Step-3: Factors of 39144

List of positive integer factors of 39144 that divides 39144 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168, 233, 466, 699, 932, 1398, 1631, 1864, 2796, 3262, 4893, 5592, 6524, 9786, 13048, 19572

Step-4: Factors of 39164

List of positive integer factors of 39164 that divides 39144 without a remainder.

1, 2, 4, 9791, 19582

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39144 and 39164. The biggest common factor number is the GCF number.
So the greatest common factor 39144 and 39164 is 4.

Also check out the Least Common Multiple of 39144 and 39164