What is the Greatest Common Factor of 74997 and 75009?

Greatest common factor (GCF) of 74997 and 75009 is 3.

GCF(74997,75009) = 3

We will now calculate the prime factors of 74997 and 75009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74997 and 75009.

How to find the GCF of 74997 and 75009?

We will first find the prime factorization of 74997 and 75009. After we will calculate the factors of 74997 and 75009 and find the biggest common factor number .

Step-1: Prime Factorization of 74997

Prime factors of 74997 are 3, 13, 641. Prime factorization of 74997 in exponential form is:

74997 = 3² × 13¹ × 641¹

Step-2: Prime Factorization of 75009

Prime factors of 75009 are 3, 11, 2273. Prime factorization of 75009 in exponential form is:

75009 = 3¹ × 11¹ × 2273¹

Step-3: Factors of 74997

List of positive integer factors of 74997 that divides 74997 without a remainder.

1, 3, 9, 13, 39, 117, 641, 1923, 5769, 8333, 24999

Step-4: Factors of 75009

List of positive integer factors of 75009 that divides 74997 without a remainder.

1, 3, 11, 33, 2273, 6819, 25003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74997 and 75009. The biggest common factor number is the GCF number.
So the greatest common factor 74997 and 75009 is 3.

Also check out the Least Common Multiple of 74997 and 75009