What is the Greatest Common Factor of 15120 and 15138?

Greatest common factor (GCF) of 15120 and 15138 is 18.

GCF(15120,15138) = 18

We will now calculate the prime factors of 15120 and 15138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15120 and 15138.

How to find the GCF of 15120 and 15138?

We will first find the prime factorization of 15120 and 15138. After we will calculate the factors of 15120 and 15138 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 15138

Prime factors of 15138 are 2, 3, 29. Prime factorization of 15138 in exponential form is:

15138 = 2¹ × 3² × 29²

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 15138

List of positive integer factors of 15138 that divides 15120 without a remainder.

1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522, 841, 1682, 2523, 5046, 7569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15120 and 15138. The biggest common factor number is the GCF number.
So the greatest common factor 15120 and 15138 is 18.

Also check out the Least Common Multiple of 15120 and 15138