What is the Greatest Common Factor of 67500 and 67518?

Greatest common factor (GCF) of 67500 and 67518 is 18.

GCF(67500,67518) = 18

We will now calculate the prime factors of 67500 and 67518, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67500 and 67518.

How to find the GCF of 67500 and 67518?

We will first find the prime factorization of 67500 and 67518. After we will calculate the factors of 67500 and 67518 and find the biggest common factor number .

Step-1: Prime Factorization of 67500

Prime factors of 67500 are 2, 3, 5. Prime factorization of 67500 in exponential form is:

67500 = 2² × 3³ × 5⁴

Step-2: Prime Factorization of 67518

Prime factors of 67518 are 2, 3, 11, 31. Prime factorization of 67518 in exponential form is:

67518 = 2¹ × 3² × 11² × 31¹

Step-3: Factors of 67500

List of positive integer factors of 67500 that divides 67500 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 125, 135, 150, 180, 225, 250, 270, 300, 375, 450, 500, 540, 625, 675, 750, 900, 1125, 1250, 1350, 1500, 1875, 2250, 2500, 2700, 3375, 3750, 4500, 5625, 6750, 7500, 11250, 13500, 16875, 22500, 33750

Step-4: Factors of 67518

List of positive integer factors of 67518 that divides 67500 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 31, 33, 62, 66, 93, 99, 121, 186, 198, 242, 279, 341, 363, 558, 682, 726, 1023, 1089, 2046, 2178, 3069, 3751, 6138, 7502, 11253, 22506, 33759

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67500 and 67518. The biggest common factor number is the GCF number.
So the greatest common factor 67500 and 67518 is 18.

Also check out the Least Common Multiple of 67500 and 67518