What is the Greatest Common Factor of 11514 and 11520?

Greatest common factor (GCF) of 11514 and 11520 is 6.

GCF(11514,11520) = 6

We will now calculate the prime factors of 11514 and 11520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11514 and 11520.

How to find the GCF of 11514 and 11520?

We will first find the prime factorization of 11514 and 11520. After we will calculate the factors of 11514 and 11520 and find the biggest common factor number .

Step-1: Prime Factorization of 11514

Prime factors of 11514 are 2, 3, 19, 101. Prime factorization of 11514 in exponential form is:

11514 = 2¹ × 3¹ × 19¹ × 101¹

Step-2: Prime Factorization of 11520

Prime factors of 11520 are 2, 3, 5. Prime factorization of 11520 in exponential form is:

11520 = 2⁸ × 3² × 5¹

Step-3: Factors of 11514

List of positive integer factors of 11514 that divides 11514 without a remainder.

1, 2, 3, 6, 19, 38, 57, 101, 114, 202, 303, 606, 1919, 3838, 5757

Step-4: Factors of 11520

List of positive integer factors of 11520 that divides 11514 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 256, 288, 320, 360, 384, 480, 576, 640, 720, 768, 960, 1152, 1280, 1440, 1920, 2304, 2880, 3840, 5760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11514 and 11520. The biggest common factor number is the GCF number.
So the greatest common factor 11514 and 11520 is 6.

Also check out the Least Common Multiple of 11514 and 11520