Greatest Common Factor of 1600 and 1608

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, 1608 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1600 and 1608 is 8.

GCF(1600,1608) = 8

GCF of 1600 and 1608

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

GCF of:
and

Greatest Common Factor of 1600 and 1608

GCF of 1600 and 1608 is 8

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 1608


2 1608
2 804
2 402
3 201
67 67
1

Prime factors of 1608 are 2,3,67. Prime factorization of 1608 in exponential form is:

1608 = 23×31×671

∴ So by taking common prime factors GCF of 1600 and 1608 is 8

Greatest Common Factor of 1600 and 1608 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 1608

List of positive integer factors of 1608 that divides 1608 without a remainder.

1,2,3,4,6,8,12,24,67,134,201,268,402,536,804,1608

Greatest Common Factor

We found the factors and prime factorization of 1600 and 1608. The biggest common factor number is the GCF number.
So the greatest common factor 1600 and 1608 is 8.

Also check out the Least Common Multiple of 1600 and 1608

Properties of GCF 1600 and 1608

(i) The GCF of 1600 and 1608 is associative

GCF of 1600 and 1608 = GCF of 1608 and 1600

Related Greatest Common Factor of 1600

Related Greatest Common Factor of 1608

Frequently Asked Questions on GCF of 1600 and 1608

1. What is the GCF of 1600 and 1608?

Answer: GCF of 1600 and 1608 is 8.

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 1608?

Answer: Factors of 1608 are 1, 2, 3, 4, 6, 8, 12, 24, 67, 134, 201, 268, 402, 536, 804, 1608. There are 16 integers that are factors of 1608. The greatest factor of 1608 is 1608.

4. How to Find the GCF of 1600 and 1608?

Answer:

Greatest Common Factor of 1600 and 1608 = 8

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 1608

1608 = 2 x 2 x 2 x 3 x 67

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

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 1600 and 1608 is 8