What is the Greatest Common Factor of 14560 and 14574?

Greatest common factor (GCF) of 14560 and 14574 is 14.

GCF(14560,14574) = 14

We will now calculate the prime factors of 14560 and 14574, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14560 and 14574.

How to find the GCF of 14560 and 14574?

We will first find the prime factorization of 14560 and 14574. After we will calculate the factors of 14560 and 14574 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 14574

Prime factors of 14574 are 2, 3, 7, 347. Prime factorization of 14574 in exponential form is:

14574 = 2¹ × 3¹ × 7¹ × 347¹

Step-3: Factors of 14560

List of positive integer factors of 14560 that divides 14560 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

Step-4: Factors of 14574

List of positive integer factors of 14574 that divides 14560 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 347, 694, 1041, 2082, 2429, 4858, 7287

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14560 and 14574. The biggest common factor number is the GCF number.
So the greatest common factor 14560 and 14574 is 14.

Also check out the Least Common Multiple of 14560 and 14574