What is the Greatest Common Factor of 1600 and 1605?

Greatest common factor (GCF) of 1600 and 1605 is 5.

GCF(1600,1605) = 5

We will now calculate the prime factors of 1600 and 1605, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1600 and 1605.

How to find the GCF of 1600 and 1605?

We will first find the prime factorization of 1600 and 1605. After we will calculate the factors of 1600 and 1605 and find the biggest common factor number .

Step-1: Prime Factorization of 1600

Prime factors of 1600 are 2, 5. Prime factorization of 1600 in exponential form is:

1600 = 2⁶ × 5²

Step-2: Prime Factorization of 1605

Prime factors of 1605 are 3, 5, 107. Prime factorization of 1605 in exponential form is:

1605 = 3¹ × 5¹ × 107¹

Step-3: Factors of 1600

List of positive integer factors of 1600 that divides 1600 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800

Step-4: Factors of 1605

List of positive integer factors of 1605 that divides 1600 without a remainder.

1, 3, 5, 15, 107, 321, 535

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1600 and 1605. The biggest common factor number is the GCF number.
So the greatest common factor 1600 and 1605 is 5.

Also check out the Least Common Multiple of 1600 and 1605