What is the Greatest Common Factor of 23730 and 23744?

Greatest common factor (GCF) of 23730 and 23744 is 14.

GCF(23730,23744) = 14

We will now calculate the prime factors of 23730 and 23744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23730 and 23744.

How to find the GCF of 23730 and 23744?

We will first find the prime factorization of 23730 and 23744. After we will calculate the factors of 23730 and 23744 and find the biggest common factor number .

Step-1: Prime Factorization of 23730

Prime factors of 23730 are 2, 3, 5, 7, 113. Prime factorization of 23730 in exponential form is:

23730 = 2¹ × 3¹ × 5¹ × 7¹ × 113¹

Step-2: Prime Factorization of 23744

Prime factors of 23744 are 2, 7, 53. Prime factorization of 23744 in exponential form is:

23744 = 2⁶ × 7¹ × 53¹

Step-3: Factors of 23730

List of positive integer factors of 23730 that divides 23730 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 113, 210, 226, 339, 565, 678, 791, 1130, 1582, 1695, 2373, 3390, 3955, 4746, 7910, 11865

Step-4: Factors of 23744

List of positive integer factors of 23744 that divides 23730 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 53, 56, 64, 106, 112, 212, 224, 371, 424, 448, 742, 848, 1484, 1696, 2968, 3392, 5936, 11872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23730 and 23744. The biggest common factor number is the GCF number.
So the greatest common factor 23730 and 23744 is 14.

Also check out the Least Common Multiple of 23730 and 23744