Greatest Common Factor of 1980 and 1984

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 1980, 1984 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1980 and 1984 is 4.

GCF(1980,1984) = 4

GCF of 1980 and 1984

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

GCF of:
and

Greatest Common Factor of 1980 and 1984

GCF of 1980 and 1984 is 4

Prime Factorization of 1980


2 1980
2 990
3 495
3 165
5 55
11 11
1

Prime factors of 1980 are 2,3,5,11. Prime factorization of 1980 in exponential form is:

1980 = 22×32×51×111

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

∴ So by taking common prime factors GCF of 1980 and 1984 is 4

Greatest Common Factor of 1980 and 1984 by matching factors method

Factors of 1980

List of positive integer factors of 1980 that divides 1980 without a remainder.

1,2,3,4,5,6,9,10,11,12,15,18,20,22,30,33,36,44,45,55,60,66,90,99,110,132,165,180,198,220,330,396,495,660,990,1980

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

Greatest Common Factor

We found the factors and prime factorization of 1980 and 1984. The biggest common factor number is the GCF number.
So the greatest common factor 1980 and 1984 is 4.

Also check out the Least Common Multiple of 1980 and 1984

Properties of GCF 1980 and 1984

(i) The GCF of 1980 and 1984 is associative

GCF of 1980 and 1984 = GCF of 1984 and 1980

Related Greatest Common Factor of 1980

Related Greatest Common Factor of 1984

Frequently Asked Questions on GCF of 1980 and 1984

1. What is the GCF of 1980 and 1984?

Answer: GCF of 1980 and 1984 is 4.

2. What are the Factors of 1980?

Answer: Factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980. There are 36 integers that are factors of 1980. The greatest factor of 1980 is 1980.

3. 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.

4. How to Find the GCF of 1980 and 1984?

Answer:

Greatest Common Factor of 1980 and 1984 = 4

Step 1: Find the prime factorization of 1980

1980 = 2 x 2 x 3 x 3 x 5 x 11

Step 2: Find the prime factorization of 1984

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

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 1980 and 1984 is 4