What is the Greatest Common Factor of 39249 and 39264?

Greatest common factor (GCF) of 39249 and 39264 is 3.

GCF(39249,39264) = 3

We will now calculate the prime factors of 39249 and 39264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39249 and 39264.

How to find the GCF of 39249 and 39264?

We will first find the prime factorization of 39249 and 39264. After we will calculate the factors of 39249 and 39264 and find the biggest common factor number .

Step-1: Prime Factorization of 39249

Prime factors of 39249 are 3, 7, 89. Prime factorization of 39249 in exponential form is:

39249 = 3² × 7² × 89¹

Step-2: Prime Factorization of 39264

Prime factors of 39264 are 2, 3, 409. Prime factorization of 39264 in exponential form is:

39264 = 2⁵ × 3¹ × 409¹

Step-3: Factors of 39249

List of positive integer factors of 39249 that divides 39249 without a remainder.

1, 3, 7, 9, 21, 49, 63, 89, 147, 267, 441, 623, 801, 1869, 4361, 5607, 13083

Step-4: Factors of 39264

List of positive integer factors of 39264 that divides 39249 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 409, 818, 1227, 1636, 2454, 3272, 4908, 6544, 9816, 13088, 19632

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39249 and 39264. The biggest common factor number is the GCF number.
So the greatest common factor 39249 and 39264 is 3.

Also check out the Least Common Multiple of 39249 and 39264