Greatest Common Factor of 1975 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 1975, 1980 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1975 and 1980 is 5.

GCF(1975,1980) = 5

GCF of 1975 and 1980

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

GCF of:
and

Greatest Common Factor of 1975 and 1980

GCF of 1975 and 1980 is 5

Prime Factorization of 1975


5 1975
5 395
79 79
1

Prime factors of 1975 are 5,79. Prime factorization of 1975 in exponential form is:

1975 = 52×791

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 1975 and 1980 is 5

Greatest Common Factor of 1975 and 1980 by matching factors method

Factors of 1975

List of positive integer factors of 1975 that divides 1975 without a remainder.

1,5,25,79,395,1975

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 1975 and 1980. The biggest common factor number is the GCF number.
So the greatest common factor 1975 and 1980 is 5.

Also check out the Least Common Multiple of 1975 and 1980

Properties of GCF 1975 and 1980

(i) The GCF of 1975 and 1980 is associative

GCF of 1975 and 1980 = GCF of 1980 and 1975

Related Greatest Common Factor of 1975

Related Greatest Common Factor of 1980

Frequently Asked Questions on GCF of 1975 and 1980

1. What is the GCF of 1975 and 1980?

Answer: GCF of 1975 and 1980 is 5.

2. What are the Factors of 1975?

Answer: Factors of 1975 are 1, 5, 25, 79, 395, 1975. There are 6 integers that are factors of 1975. The greatest factor of 1975 is 1975.

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 1975 and 1980?

Answer:

Greatest Common Factor of 1975 and 1980 = 5

Step 1: Find the prime factorization of 1975

1975 = 5 x 5 x 79

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 = 5

Step 4: Therefore, the greatest common factor of 1975 and 1980 is 5