Greatest Common Factor of 1996 and 2000

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 1996, 2000 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1996 and 2000 is 4.

GCF(1996,2000) = 4

GCF of 1996 and 2000

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

GCF of:
and

Greatest Common Factor of 1996 and 2000

GCF of 1996 and 2000 is 4

Prime Factorization of 1996


2 1996
2 998
499 499
1

Prime factors of 1996 are 2,499. Prime factorization of 1996 in exponential form is:

1996 = 22×4991

Prime Factorization of 2000


2 2000
2 1000
2 500
2 250
5 125
5 25
5 5
1

Prime factors of 2000 are 2,5. Prime factorization of 2000 in exponential form is:

2000 = 24×53

∴ So by taking common prime factors GCF of 1996 and 2000 is 4

Greatest Common Factor of 1996 and 2000 by matching factors method

Factors of 1996

List of positive integer factors of 1996 that divides 1996 without a remainder.

1,2,4,499,998,1996

Factors of 2000

List of positive integer factors of 2000 that divides 2000 without a remainder.

1,2,4,5,8,10,16,20,25,40,50,80,100,125,200,250,400,500,1000,2000

Greatest Common Factor

We found the factors and prime factorization of 1996 and 2000. The biggest common factor number is the GCF number.
So the greatest common factor 1996 and 2000 is 4.

Also check out the Least Common Multiple of 1996 and 2000

Properties of GCF 1996 and 2000

(i) The GCF of 1996 and 2000 is associative

GCF of 1996 and 2000 = GCF of 2000 and 1996

Related Greatest Common Factor of 1996

Related Greatest Common Factor of 2000

Frequently Asked Questions on GCF of 1996 and 2000

1. What is the GCF of 1996 and 2000?

Answer: GCF of 1996 and 2000 is 4.

2. What are the Factors of 1996?

Answer: Factors of 1996 are 1, 2, 4, 499, 998, 1996. There are 6 integers that are factors of 1996. The greatest factor of 1996 is 1996.

3. What are the Factors of 2000?

Answer: Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000. There are 20 integers that are factors of 2000. The greatest factor of 2000 is 2000.

4. How to Find the GCF of 1996 and 2000?

Answer:

Greatest Common Factor of 1996 and 2000 = 4

Step 1: Find the prime factorization of 1996

1996 = 2 x 2 x 499

Step 2: Find the prime factorization of 2000

2000 = 2 x 2 x 2 x 2 x 5 x 5 x 5

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 1996 and 2000 is 4