Greatest Common Factor of 1600 and 1605

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 1600, 1605 i.e. 5 largest integer by which both the numbers can be divided.

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

GCF(1600,1605) = 5

GCF of 1600 and 1605

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 1600 and 1605

GCF of 1600 and 1605 is 5

Prime Factorization of 1600


2 1600
2 800
2 400
2 200
2 100
2 50
5 25
5 5
1

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

1600 = 26×52

Prime Factorization of 1605


3 1605
5 535
107 107
1

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

1605 = 31×51×1071

∴ So by taking common prime factors GCF of 1600 and 1605 is 5

Greatest Common Factor of 1600 and 1605 by matching factors method

Factors of 1600

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

1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,160,200,320,400,800,1600

Factors of 1605

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

1,3,5,15,107,321,535,1605

Greatest Common Factor

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

Properties of GCF 1600 and 1605

(i) The GCF of 1600 and 1605 is associative

GCF of 1600 and 1605 = GCF of 1605 and 1600

Related Greatest Common Factor of 1600

Related Greatest Common Factor of 1605

Frequently Asked Questions on GCF of 1600 and 1605

1. What is the GCF of 1600 and 1605?

Answer: GCF of 1600 and 1605 is 5.

2. What are the Factors of 1600?

Answer: Factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600. There are 21 integers that are factors of 1600. The greatest factor of 1600 is 1600.

3. What are the Factors of 1605?

Answer: Factors of 1605 are 1, 3, 5, 15, 107, 321, 535, 1605. There are 8 integers that are factors of 1605. The greatest factor of 1605 is 1605.

4. How to Find the GCF of 1600 and 1605?

Answer:

Greatest Common Factor of 1600 and 1605 = 5

Step 1: Find the prime factorization of 1600

1600 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 1605

1605 = 3 x 5 x 107

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 5

Step 4: Therefore, the greatest common factor of 1600 and 1605 is 5