What is the Greatest Common Factor of 67785 and 67800?

Greatest common factor (GCF) of 67785 and 67800 is 15.

GCF(67785,67800) = 15

We will now calculate the prime factors of 67785 and 67800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67785 and 67800.

How to find the GCF of 67785 and 67800?

We will first find the prime factorization of 67785 and 67800. After we will calculate the factors of 67785 and 67800 and find the biggest common factor number .

Step-1: Prime Factorization of 67785

Prime factors of 67785 are 3, 5, 4519. Prime factorization of 67785 in exponential form is:

67785 = 3¹ × 5¹ × 4519¹

Step-2: Prime Factorization of 67800

Prime factors of 67800 are 2, 3, 5, 113. Prime factorization of 67800 in exponential form is:

67800 = 2³ × 3¹ × 5² × 113¹

Step-3: Factors of 67785

List of positive integer factors of 67785 that divides 67785 without a remainder.

1, 3, 5, 15, 4519, 13557, 22595

Step-4: Factors of 67800

List of positive integer factors of 67800 that divides 67785 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 113, 120, 150, 200, 226, 300, 339, 452, 565, 600, 678, 904, 1130, 1356, 1695, 2260, 2712, 2825, 3390, 4520, 5650, 6780, 8475, 11300, 13560, 16950, 22600, 33900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67785 and 67800. The biggest common factor number is the GCF number.
So the greatest common factor 67785 and 67800 is 15.

Also check out the Least Common Multiple of 67785 and 67800