Greatest Common Factor of 1972 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 1972, 1980 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1972 and 1980 is 4.

GCF(1972,1980) = 4

GCF of 1972 and 1980

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

GCF of:
and

Greatest Common Factor of 1972 and 1980

GCF of 1972 and 1980 is 4

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 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 1972 and 1980 is 4

Greatest Common Factor of 1972 and 1980 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 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 1972 and 1980. The biggest common factor number is the GCF number.
So the greatest common factor 1972 and 1980 is 4.

Also check out the Least Common Multiple of 1972 and 1980

Properties of GCF 1972 and 1980

(i) The GCF of 1972 and 1980 is associative

GCF of 1972 and 1980 = GCF of 1980 and 1972

Related Greatest Common Factor of 1972

Related Greatest Common Factor of 1980

Frequently Asked Questions on GCF of 1972 and 1980

1. What is the GCF of 1972 and 1980?

Answer: GCF of 1972 and 1980 is 4.

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 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 1972 and 1980?

Answer:

Greatest Common Factor of 1972 and 1980 = 4

Step 1: Find the prime factorization of 1972

1972 = 2 x 2 x 17 x 29

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 2 = 4

Step 4: Therefore, the greatest common factor of 1972 and 1980 is 4