Greatest Common Factor of 9972 and 9975

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 9972, 9975 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 9972 and 9975 is 3.

GCF(9972,9975) = 3

GCF of 9972 and 9975

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

GCF of:
and

Greatest Common Factor of 9972 and 9975

GCF of 9972 and 9975 is 3

Prime Factorization of 9972


2 9972
2 4986
3 2493
3 831
277 277
1

Prime factors of 9972 are 2,3,277. Prime factorization of 9972 in exponential form is:

9972 = 22×32×2771

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

∴ So by taking common prime factors GCF of 9972 and 9975 is 3

Greatest Common Factor of 9972 and 9975 by matching factors method

Factors of 9972

List of positive integer factors of 9972 that divides 9972 without a remainder.

1,2,3,4,6,9,12,18,36,277,554,831,1108,1662,2493,3324,4986,9972

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

Greatest Common Factor

We found the factors and prime factorization of 9972 and 9975. The biggest common factor number is the GCF number.
So the greatest common factor 9972 and 9975 is 3.

Also check out the Least Common Multiple of 9972 and 9975

Properties of GCF 9972 and 9975

(i) The GCF of 9972 and 9975 is associative

GCF of 9972 and 9975 = GCF of 9975 and 9972

Related Greatest Common Factor of 9972

Related Greatest Common Factor of 9975

Frequently Asked Questions on GCF of 9972 and 9975

1. What is the GCF of 9972 and 9975?

Answer: GCF of 9972 and 9975 is 3.

2. What are the Factors of 9972?

Answer: Factors of 9972 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972. There are 18 integers that are factors of 9972. The greatest factor of 9972 is 9972.

3. 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.

4. How to Find the GCF of 9972 and 9975?

Answer:

Greatest Common Factor of 9972 and 9975 = 3

Step 1: Find the prime factorization of 9972

9972 = 2 x 2 x 3 x 3 x 277

Step 2: Find the prime factorization of 9975

9975 = 3 x 5 x 5 x 7 x 19

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

GCF = 3

Step 4: Therefore, the greatest common factor of 9972 and 9975 is 3