What is the Greatest Common Factor of 23699 and 23712?

Greatest common factor (GCF) of 23699 and 23712 is 13.

GCF(23699,23712) = 13

We will now calculate the prime factors of 23699 and 23712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23699 and 23712.

How to find the GCF of 23699 and 23712?

We will first find the prime factorization of 23699 and 23712. After we will calculate the factors of 23699 and 23712 and find the biggest common factor number .

Step-1: Prime Factorization of 23699

Prime factors of 23699 are 13, 1823. Prime factorization of 23699 in exponential form is:

23699 = 13¹ × 1823¹

Step-2: Prime Factorization of 23712

Prime factors of 23712 are 2, 3, 13, 19. Prime factorization of 23712 in exponential form is:

23712 = 2⁵ × 3¹ × 13¹ × 19¹

Step-3: Factors of 23699

List of positive integer factors of 23699 that divides 23699 without a remainder.

1, 13, 1823

Step-4: Factors of 23712

List of positive integer factors of 23712 that divides 23699 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 19, 24, 26, 32, 38, 39, 48, 52, 57, 76, 78, 96, 104, 114, 152, 156, 208, 228, 247, 304, 312, 416, 456, 494, 608, 624, 741, 912, 988, 1248, 1482, 1824, 1976, 2964, 3952, 5928, 7904, 11856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23699 and 23712. The biggest common factor number is the GCF number.
So the greatest common factor 23699 and 23712 is 13.

Also check out the Least Common Multiple of 23699 and 23712