Greatest Common Factor of 1997 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 1997, 2000 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1997 and 2000 is 1.

GCF(1997,2000) = 1

GCF of 1997 and 2000

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

GCF of:
and

Greatest Common Factor of 1997 and 2000

GCF of 1997 and 2000 is 1

Prime Factorization of 1997


1997 1997
1

Prime factors of 1997 are 1997. Prime factorization of 1997 in exponential form is:

1997 = 19971

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.Prime factorization of 2000 in exponential form is:

2000 = 24×53

∴ So by taking common prime factors GCF of 1997 and 2000 is 1

Greatest Common Factor of 1997 and 2000 by matching factors method

Factors of 1997

List of positive integer factors of 1997 that divides 1997 without a remainder.

1,1997

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 1997 and 2000. The biggest common factor number is the GCF number.
So the greatest common factor 1997 and 2000 is 1.

Also check out the Least Common Multiple of 1997 and 2000

Properties of GCF 1997 and 2000

(i) The GCF of 1997 and 2000 is associative

GCF of 1997 and 2000 = GCF of 2000 and 1997

Related Greatest Common Factor of 1997

Related Greatest Common Factor of 2000

Frequently Asked Questions on GCF of 1997 and 2000

1. What is the GCF of 1997 and 2000?

Answer: GCF of 1997 and 2000 is 1.

2. What are the Factors of 1997?

Answer: Factors of 1997 are 1, 1997. There are 2 integers that are factors of 1997. The greatest factor of 1997 is 1997.

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 1997 and 2000?

Answer:

Greatest Common Factor of 1997 and 2000 = 1

Step 1: Find the prime factorization of 1997

1997 = 1997

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 = = 1

Step 4: Therefore, the greatest common factor of 1997 and 2000 is 1