What is the Greatest Common Factor of 15120 and 15140?

Greatest common factor (GCF) of 15120 and 15140 is 20.

GCF(15120,15140) = 20

We will now calculate the prime factors of 15120 and 15140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15120 and 15140.

How to find the GCF of 15120 and 15140?

We will first find the prime factorization of 15120 and 15140. After we will calculate the factors of 15120 and 15140 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 15140

Prime factors of 15140 are 2, 5, 757. Prime factorization of 15140 in exponential form is:

15140 = 2² × 5¹ × 757¹

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 15140

List of positive integer factors of 15140 that divides 15120 without a remainder.

1, 2, 4, 5, 10, 20, 757, 1514, 3028, 3785, 7570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15120 and 15140. The biggest common factor number is the GCF number.
So the greatest common factor 15120 and 15140 is 20.

Also check out the Least Common Multiple of 15120 and 15140