Greatest Common Factor of 1974 and 1980

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 1974, 1980 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1974 and 1980 is 6.

GCF(1974,1980) = 6

GCF of 1974 and 1980

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

GCF of:
and

Greatest Common Factor of 1974 and 1980

GCF of 1974 and 1980 is 6

Prime Factorization of 1974


2 1974
3 987
7 329
47 47
1

Prime factors of 1974 are 2,3,7,47. Prime factorization of 1974 in exponential form is:

1974 = 21×31×71×471

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

∴ So by taking common prime factors GCF of 1974 and 1980 is 6

Greatest Common Factor of 1974 and 1980 by matching factors method

Factors of 1974

List of positive integer factors of 1974 that divides 1974 without a remainder.

1,2,3,6,7,14,21,42,47,94,141,282,329,658,987,1974

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

Greatest Common Factor

We found the factors and prime factorization of 1974 and 1980. The biggest common factor number is the GCF number.
So the greatest common factor 1974 and 1980 is 6.

Also check out the Least Common Multiple of 1974 and 1980

Properties of GCF 1974 and 1980

(i) The GCF of 1974 and 1980 is associative

GCF of 1974 and 1980 = GCF of 1980 and 1974

Related Greatest Common Factor of 1974

Related Greatest Common Factor of 1980

Frequently Asked Questions on GCF of 1974 and 1980

1. What is the GCF of 1974 and 1980?

Answer: GCF of 1974 and 1980 is 6.

2. What are the Factors of 1974?

Answer: Factors of 1974 are 1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987, 1974. There are 16 integers that are factors of 1974. The greatest factor of 1974 is 1974.

3. 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.

4. How to Find the GCF of 1974 and 1980?

Answer:

Greatest Common Factor of 1974 and 1980 = 6

Step 1: Find the prime factorization of 1974

1974 = 2 x 3 x 7 x 47

Step 2: Find the prime factorization of 1980

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

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 1974 and 1980 is 6