Greatest Common Factor of 1972 and 1978

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 1972, 1978 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1972 and 1978 is 2.

GCF(1972,1978) = 2

GCF of 1972 and 1978

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

GCF of:
and

Greatest Common Factor of 1972 and 1978

GCF of 1972 and 1978 is 2

Prime Factorization of 1972


2 1972
2 986
17 493
29 29
1

Prime factors of 1972 are 2,17,29. Prime factorization of 1972 in exponential form is:

1972 = 22×171×291

Prime Factorization of 1978


2 1978
23 989
43 43
1

Prime factors of 1978 are 2,23,43. Prime factorization of 1978 in exponential form is:

1978 = 21×231×431

∴ So by taking common prime factors GCF of 1972 and 1978 is 2

Greatest Common Factor of 1972 and 1978 by matching factors method

Factors of 1972

List of positive integer factors of 1972 that divides 1972 without a remainder.

1,2,4,17,29,34,58,68,116,493,986,1972

Factors of 1978

List of positive integer factors of 1978 that divides 1978 without a remainder.

1,2,23,43,46,86,989,1978

Greatest Common Factor

We found the factors and prime factorization of 1972 and 1978. The biggest common factor number is the GCF number.
So the greatest common factor 1972 and 1978 is 2.

Also check out the Least Common Multiple of 1972 and 1978

Properties of GCF 1972 and 1978

(i) The GCF of 1972 and 1978 is associative

GCF of 1972 and 1978 = GCF of 1978 and 1972

Related Greatest Common Factor of 1972

Related Greatest Common Factor of 1978

Frequently Asked Questions on GCF of 1972 and 1978

1. What is the GCF of 1972 and 1978?

Answer: GCF of 1972 and 1978 is 2.

2. What are the Factors of 1972?

Answer: Factors of 1972 are 1, 2, 4, 17, 29, 34, 58, 68, 116, 493, 986, 1972. There are 12 integers that are factors of 1972. The greatest factor of 1972 is 1972.

3. What are the Factors of 1978?

Answer: Factors of 1978 are 1, 2, 23, 43, 46, 86, 989, 1978. There are 8 integers that are factors of 1978. The greatest factor of 1978 is 1978.

4. How to Find the GCF of 1972 and 1978?

Answer:

Greatest Common Factor of 1972 and 1978 = 2

Step 1: Find the prime factorization of 1972

1972 = 2 x 2 x 17 x 29

Step 2: Find the prime factorization of 1978

1978 = 2 x 23 x 43

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 1972 and 1978 is 2