What is the Greatest Common Factor of 23289 and 23296?

Greatest common factor (GCF) of 23289 and 23296 is 7.

GCF(23289,23296) = 7

We will now calculate the prime factors of 23289 and 23296, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23289 and 23296.

How to find the GCF of 23289 and 23296?

We will first find the prime factorization of 23289 and 23296. After we will calculate the factors of 23289 and 23296 and find the biggest common factor number .

Step-1: Prime Factorization of 23289

Prime factors of 23289 are 3, 7, 1109. Prime factorization of 23289 in exponential form is:

23289 = 3¹ × 7¹ × 1109¹

Step-2: Prime Factorization of 23296

Prime factors of 23296 are 2, 7, 13. Prime factorization of 23296 in exponential form is:

23296 = 2⁸ × 7¹ × 13¹

Step-3: Factors of 23289

List of positive integer factors of 23289 that divides 23289 without a remainder.

1, 3, 7, 21, 1109, 3327, 7763

Step-4: Factors of 23296

List of positive integer factors of 23296 that divides 23289 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 64, 91, 104, 112, 128, 182, 208, 224, 256, 364, 416, 448, 728, 832, 896, 1456, 1664, 1792, 2912, 3328, 5824, 11648

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23289 and 23296. The biggest common factor number is the GCF number.
So the greatest common factor 23289 and 23296 is 7.

Also check out the Least Common Multiple of 23289 and 23296