What is the Greatest Common Factor of 1604 and 1614?

Greatest common factor (GCF) of 1604 and 1614 is 2.

GCF(1604,1614) = 2

We will now calculate the prime factors of 1604 and 1614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1604 and 1614.

How to find the GCF of 1604 and 1614?

We will first find the prime factorization of 1604 and 1614. After we will calculate the factors of 1604 and 1614 and find the biggest common factor number .

Step-1: Prime Factorization of 1604

Prime factors of 1604 are 2, 401. Prime factorization of 1604 in exponential form is:

1604 = 2² × 401¹

Step-2: Prime Factorization of 1614

Prime factors of 1614 are 2, 3, 269. Prime factorization of 1614 in exponential form is:

1614 = 2¹ × 3¹ × 269¹

Step-3: Factors of 1604

List of positive integer factors of 1604 that divides 1604 without a remainder.

1, 2, 4, 401, 802

Step-4: Factors of 1614

List of positive integer factors of 1614 that divides 1604 without a remainder.

1, 2, 3, 6, 269, 538, 807

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1604 and 1614. The biggest common factor number is the GCF number.
So the greatest common factor 1604 and 1614 is 2.

Also check out the Least Common Multiple of 1604 and 1614