What is the Greatest Common Factor of 23744 and 23758?

Greatest common factor (GCF) of 23744 and 23758 is 14.

GCF(23744,23758) = 14

We will now calculate the prime factors of 23744 and 23758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23744 and 23758.

How to find the GCF of 23744 and 23758?

We will first find the prime factorization of 23744 and 23758. After we will calculate the factors of 23744 and 23758 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 23758

Prime factors of 23758 are 2, 7, 1697. Prime factorization of 23758 in exponential form is:

23758 = 2¹ × 7¹ × 1697¹

Step-3: Factors of 23744

List of positive integer factors of 23744 that divides 23744 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

Step-4: Factors of 23758

List of positive integer factors of 23758 that divides 23744 without a remainder.

1, 2, 7, 14, 1697, 3394, 11879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23744 and 23758. The biggest common factor number is the GCF number.
So the greatest common factor 23744 and 23758 is 14.

Also check out the Least Common Multiple of 23744 and 23758