What is the Greatest Common Factor of 14548 and 14560?

Greatest common factor (GCF) of 14548 and 14560 is 4.

GCF(14548,14560) = 4

We will now calculate the prime factors of 14548 and 14560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14548 and 14560.

How to find the GCF of 14548 and 14560?

We will first find the prime factorization of 14548 and 14560. After we will calculate the factors of 14548 and 14560 and find the biggest common factor number .

Step-1: Prime Factorization of 14548

Prime factors of 14548 are 2, 3637. Prime factorization of 14548 in exponential form is:

14548 = 2² × 3637¹

Step-2: Prime Factorization of 14560

Prime factors of 14560 are 2, 5, 7, 13. Prime factorization of 14560 in exponential form is:

14560 = 2⁵ × 5¹ × 7¹ × 13¹

Step-3: Factors of 14548

List of positive integer factors of 14548 that divides 14548 without a remainder.

1, 2, 4, 3637, 7274

Step-4: Factors of 14560

List of positive integer factors of 14560 that divides 14548 without a remainder.

1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 26, 28, 32, 35, 40, 52, 56, 65, 70, 80, 91, 104, 112, 130, 140, 160, 182, 208, 224, 260, 280, 364, 416, 455, 520, 560, 728, 910, 1040, 1120, 1456, 1820, 2080, 2912, 3640, 7280

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14548 and 14560. The biggest common factor number is the GCF number.
So the greatest common factor 14548 and 14560 is 4.

Also check out the Least Common Multiple of 14548 and 14560