What is the Greatest Common Factor of 74686 and 74700?

Greatest common factor (GCF) of 74686 and 74700 is 2.

GCF(74686,74700) = 2

We will now calculate the prime factors of 74686 and 74700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74686 and 74700.

How to find the GCF of 74686 and 74700?

We will first find the prime factorization of 74686 and 74700. After we will calculate the factors of 74686 and 74700 and find the biggest common factor number .

Step-1: Prime Factorization of 74686

Prime factors of 74686 are 2, 107, 349. Prime factorization of 74686 in exponential form is:

74686 = 2¹ × 107¹ × 349¹

Step-2: 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-3: Factors of 74686

List of positive integer factors of 74686 that divides 74686 without a remainder.

1, 2, 107, 214, 349, 698, 37343

Step-4: Factors of 74700

List of positive integer factors of 74700 that divides 74686 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74686 and 74700. The biggest common factor number is the GCF number.
So the greatest common factor 74686 and 74700 is 2.

Also check out the Least Common Multiple of 74686 and 74700