Greatest Common Factor of 1974 and 1982

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, 1982 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1974 and 1982 is 2.

GCF(1974,1982) = 2

GCF of 1974 and 1982

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

GCF of:
and

Greatest Common Factor of 1974 and 1982

GCF of 1974 and 1982 is 2

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 1982


2 1982
991 991
1

Prime factors of 1982 are 2,991. Prime factorization of 1982 in exponential form is:

1982 = 21×9911

∴ So by taking common prime factors GCF of 1974 and 1982 is 2

Greatest Common Factor of 1974 and 1982 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 1982

List of positive integer factors of 1982 that divides 1982 without a remainder.

1,2,991,1982

Greatest Common Factor

We found the factors and prime factorization of 1974 and 1982. The biggest common factor number is the GCF number.
So the greatest common factor 1974 and 1982 is 2.

Also check out the Least Common Multiple of 1974 and 1982

Properties of GCF 1974 and 1982

(i) The GCF of 1974 and 1982 is associative

GCF of 1974 and 1982 = GCF of 1982 and 1974

Related Greatest Common Factor of 1974

Related Greatest Common Factor of 1982

Frequently Asked Questions on GCF of 1974 and 1982

1. What is the GCF of 1974 and 1982?

Answer: GCF of 1974 and 1982 is 2.

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 1982?

Answer: Factors of 1982 are 1, 2, 991, 1982. There are 4 integers that are factors of 1982. The greatest factor of 1982 is 1982.

4. How to Find the GCF of 1974 and 1982?

Answer:

Greatest Common Factor of 1974 and 1982 = 2

Step 1: Find the prime factorization of 1974

1974 = 2 x 3 x 7 x 47

Step 2: Find the prime factorization of 1982

1982 = 2 x 991

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 1974 and 1982 is 2