Greatest Common Factor of 1984 and 1990

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 1984, 1990 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1984 and 1990 is 2.

GCF(1984,1990) = 2

GCF of 1984 and 1990

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

GCF of:
and

Greatest Common Factor of 1984 and 1990

GCF of 1984 and 1990 is 2

Prime Factorization of 1984


2 1984
2 992
2 496
2 248
2 124
2 62
31 31
1

Prime factors of 1984 are 2,31. Prime factorization of 1984 in exponential form is:

1984 = 26×311

Prime Factorization of 1990


2 1990
5 995
199 199
1

Prime factors of 1990 are 2,5,199. Prime factorization of 1990 in exponential form is:

1990 = 21×51×1991

∴ So by taking common prime factors GCF of 1984 and 1990 is 2

Greatest Common Factor of 1984 and 1990 by matching factors method

Factors of 1984

List of positive integer factors of 1984 that divides 1984 without a remainder.

1,2,4,8,16,31,32,62,64,124,248,496,992,1984

Factors of 1990

List of positive integer factors of 1990 that divides 1990 without a remainder.

1,2,5,10,199,398,995,1990

Greatest Common Factor

We found the factors and prime factorization of 1984 and 1990. The biggest common factor number is the GCF number.
So the greatest common factor 1984 and 1990 is 2.

Also check out the Least Common Multiple of 1984 and 1990

Properties of GCF 1984 and 1990

(i) The GCF of 1984 and 1990 is associative

GCF of 1984 and 1990 = GCF of 1990 and 1984

Related Greatest Common Factor of 1984

Related Greatest Common Factor of 1990

Frequently Asked Questions on GCF of 1984 and 1990

1. What is the GCF of 1984 and 1990?

Answer: GCF of 1984 and 1990 is 2.

2. What are the Factors of 1984?

Answer: Factors of 1984 are 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992, 1984. There are 14 integers that are factors of 1984. The greatest factor of 1984 is 1984.

3. What are the Factors of 1990?

Answer: Factors of 1990 are 1, 2, 5, 10, 199, 398, 995, 1990. There are 8 integers that are factors of 1990. The greatest factor of 1990 is 1990.

4. How to Find the GCF of 1984 and 1990?

Answer:

Greatest Common Factor of 1984 and 1990 = 2

Step 1: Find the prime factorization of 1984

1984 = 2 x 2 x 2 x 2 x 2 x 2 x 31

Step 2: Find the prime factorization of 1990

1990 = 2 x 5 x 199

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

GCF = 2

Step 4: Therefore, the greatest common factor of 1984 and 1990 is 2