Greatest Common Factor of 1967 and 1974

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 1967, 1974 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1967 and 1974 is 7.

GCF(1967,1974) = 7

GCF of 1967 and 1974

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

GCF of:
and

Greatest Common Factor of 1967 and 1974

GCF of 1967 and 1974 is 7

Prime Factorization of 1967


7 1967
281 281
1

Prime factors of 1967 are 7,281. Prime factorization of 1967 in exponential form is:

1967 = 71×2811

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

∴ So by taking common prime factors GCF of 1967 and 1974 is 7

Greatest Common Factor of 1967 and 1974 by matching factors method

Factors of 1967

List of positive integer factors of 1967 that divides 1967 without a remainder.

1,7,281,1967

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

Greatest Common Factor

We found the factors and prime factorization of 1967 and 1974. The biggest common factor number is the GCF number.
So the greatest common factor 1967 and 1974 is 7.

Also check out the Least Common Multiple of 1967 and 1974

Properties of GCF 1967 and 1974

(i) The GCF of 1967 and 1974 is associative

GCF of 1967 and 1974 = GCF of 1974 and 1967

Related Greatest Common Factor of 1967

Related Greatest Common Factor of 1974

Frequently Asked Questions on GCF of 1967 and 1974

1. What is the GCF of 1967 and 1974?

Answer: GCF of 1967 and 1974 is 7.

2. What are the Factors of 1967?

Answer: Factors of 1967 are 1, 7, 281, 1967. There are 4 integers that are factors of 1967. The greatest factor of 1967 is 1967.

3. 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.

4. How to Find the GCF of 1967 and 1974?

Answer:

Greatest Common Factor of 1967 and 1974 = 7

Step 1: Find the prime factorization of 1967

1967 = 7 x 281

Step 2: Find the prime factorization of 1974

1974 = 2 x 3 x 7 x 47

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

GCF = 7

Step 4: Therefore, the greatest common factor of 1967 and 1974 is 7