Greatest Common Factor of 9975 and 9982

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 9975, 9982 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 9975 and 9982 is 7.

GCF(9975,9982) = 7

GCF of 9975 and 9982

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

GCF of:
and

Greatest Common Factor of 9975 and 9982

GCF of 9975 and 9982 is 7

Prime Factorization of 9975


3 9975
5 3325
5 665
7 133
19 19
1

Prime factors of 9975 are 3,5,7,19. Prime factorization of 9975 in exponential form is:

9975 = 31×52×71×191

Prime Factorization of 9982


2 9982
7 4991
23 713
31 31
1

Prime factors of 9982 are 2,7,23,31. Prime factorization of 9982 in exponential form is:

9982 = 21×71×231×311

∴ So by taking common prime factors GCF of 9975 and 9982 is 7

Greatest Common Factor of 9975 and 9982 by matching factors method

Factors of 9975

List of positive integer factors of 9975 that divides 9975 without a remainder.

1,3,5,7,15,19,21,25,35,57,75,95,105,133,175,285,399,475,525,665,1425,1995,3325,9975

Factors of 9982

List of positive integer factors of 9982 that divides 9982 without a remainder.

1,2,7,14,23,31,46,62,161,217,322,434,713,1426,4991,9982

Greatest Common Factor

We found the factors and prime factorization of 9975 and 9982. The biggest common factor number is the GCF number.
So the greatest common factor 9975 and 9982 is 7.

Also check out the Least Common Multiple of 9975 and 9982

Properties of GCF 9975 and 9982

(i) The GCF of 9975 and 9982 is associative

GCF of 9975 and 9982 = GCF of 9982 and 9975

Related Greatest Common Factor of 9975

Related Greatest Common Factor of 9982

Frequently Asked Questions on GCF of 9975 and 9982

1. What is the GCF of 9975 and 9982?

Answer: GCF of 9975 and 9982 is 7.

2. What are the Factors of 9975?

Answer: Factors of 9975 are 1, 3, 5, 7, 15, 19, 21, 25, 35, 57, 75, 95, 105, 133, 175, 285, 399, 475, 525, 665, 1425, 1995, 3325, 9975. There are 24 integers that are factors of 9975. The greatest factor of 9975 is 9975.

3. What are the Factors of 9982?

Answer: Factors of 9982 are 1, 2, 7, 14, 23, 31, 46, 62, 161, 217, 322, 434, 713, 1426, 4991, 9982. There are 16 integers that are factors of 9982. The greatest factor of 9982 is 9982.

4. How to Find the GCF of 9975 and 9982?

Answer:

Greatest Common Factor of 9975 and 9982 = 7

Step 1: Find the prime factorization of 9975

9975 = 3 x 5 x 5 x 7 x 19

Step 2: Find the prime factorization of 9982

9982 = 2 x 7 x 23 x 31

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 9975 and 9982 is 7