What is the Greatest Common Factor of 15120 and 15134?

Greatest common factor (GCF) of 15120 and 15134 is 14.

GCF(15120,15134) = 14

We will now calculate the prime factors of 15120 and 15134, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15120 and 15134.

How to find the GCF of 15120 and 15134?

We will first find the prime factorization of 15120 and 15134. After we will calculate the factors of 15120 and 15134 and find the biggest common factor number .

Step-1: Prime Factorization of 15120

Prime factors of 15120 are 2, 3, 5, 7. Prime factorization of 15120 in exponential form is:

15120 = 2⁴ × 3³ × 5¹ × 7¹

Step-2: Prime Factorization of 15134

Prime factors of 15134 are 2, 7, 23, 47. Prime factorization of 15134 in exponential form is:

15134 = 2¹ × 7¹ × 23¹ × 47¹

Step-3: Factors of 15120

List of positive integer factors of 15120 that divides 15120 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 84, 90, 105, 108, 112, 120, 126, 135, 140, 144, 168, 180, 189, 210, 216, 240, 252, 270, 280, 315, 336, 360, 378, 420, 432, 504, 540, 560, 630, 720, 756, 840, 945, 1008, 1080, 1260, 1512, 1680, 1890, 2160, 2520, 3024, 3780, 5040, 7560

Step-4: Factors of 15134

List of positive integer factors of 15134 that divides 15120 without a remainder.

1, 2, 7, 14, 23, 46, 47, 94, 161, 322, 329, 658, 1081, 2162, 7567

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15120 and 15134. The biggest common factor number is the GCF number.
So the greatest common factor 15120 and 15134 is 14.

Also check out the Least Common Multiple of 15120 and 15134