What is the Greatest Common Factor of 74700 and 74709?

Greatest common factor (GCF) of 74700 and 74709 is 9.

GCF(74700,74709) = 9

We will now calculate the prime factors of 74700 and 74709, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74700 and 74709.

How to find the GCF of 74700 and 74709?

We will first find the prime factorization of 74700 and 74709. After we will calculate the factors of 74700 and 74709 and find the biggest common factor number .

Step-1: Prime Factorization of 74700

Prime factors of 74700 are 2, 3, 5, 83. Prime factorization of 74700 in exponential form is:

74700 = 2² × 3² × 5² × 83¹

Step-2: Prime Factorization of 74709

Prime factors of 74709 are 3, 2767. Prime factorization of 74709 in exponential form is:

74709 = 3³ × 2767¹

Step-3: Factors of 74700

List of positive integer factors of 74700 that divides 74700 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 83, 90, 100, 150, 166, 180, 225, 249, 300, 332, 415, 450, 498, 747, 830, 900, 996, 1245, 1494, 1660, 2075, 2490, 2988, 3735, 4150, 4980, 6225, 7470, 8300, 12450, 14940, 18675, 24900, 37350

Step-4: Factors of 74709

List of positive integer factors of 74709 that divides 74700 without a remainder.

1, 3, 9, 27, 2767, 8301, 24903

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74700 and 74709. The biggest common factor number is the GCF number.
So the greatest common factor 74700 and 74709 is 9.

Also check out the Least Common Multiple of 74700 and 74709