Greatest Common Factor of 9724 and 9728

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 9724, 9728 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 9724 and 9728 is 4.

GCF(9724,9728) = 4

GCF of 9724 and 9728

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

GCF of:
and

Greatest Common Factor of 9724 and 9728

GCF of 9724 and 9728 is 4

Prime Factorization of 9724


2 9724
2 4862
11 2431
13 221
17 17
1

Prime factors of 9724 are 2,11,13,17. Prime factorization of 9724 in exponential form is:

9724 = 22×111×131×171

Prime Factorization of 9728


2 9728
2 4864
2 2432
2 1216
2 608
2 304
2 152
2 76
2 38
19 19
1

Prime factors of 9728 are 2,19. Prime factorization of 9728 in exponential form is:

9728 = 29×191

∴ So by taking common prime factors GCF of 9724 and 9728 is 4

Greatest Common Factor of 9724 and 9728 by matching factors method

Factors of 9724

List of positive integer factors of 9724 that divides 9724 without a remainder.

1,2,4,11,13,17,22,26,34,44,52,68,143,187,221,286,374,442,572,748,884,2431,4862,9724

Factors of 9728

List of positive integer factors of 9728 that divides 9728 without a remainder.

1,2,4,8,16,19,32,38,64,76,128,152,256,304,512,608,1216,2432,4864,9728

Greatest Common Factor

We found the factors and prime factorization of 9724 and 9728. The biggest common factor number is the GCF number.
So the greatest common factor 9724 and 9728 is 4.

Also check out the Least Common Multiple of 9724 and 9728

Properties of GCF 9724 and 9728

(i) The GCF of 9724 and 9728 is associative

GCF of 9724 and 9728 = GCF of 9728 and 9724

Related Greatest Common Factor of 9724

Related Greatest Common Factor of 9728

Frequently Asked Questions on GCF of 9724 and 9728

1. What is the GCF of 9724 and 9728?

Answer: GCF of 9724 and 9728 is 4.

2. What are the Factors of 9724?

Answer: Factors of 9724 are 1, 2, 4, 11, 13, 17, 22, 26, 34, 44, 52, 68, 143, 187, 221, 286, 374, 442, 572, 748, 884, 2431, 4862, 9724. There are 24 integers that are factors of 9724. The greatest factor of 9724 is 9724.

3. What are the Factors of 9728?

Answer: Factors of 9728 are 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1216, 2432, 4864, 9728. There are 20 integers that are factors of 9728. The greatest factor of 9728 is 9728.

4. How to Find the GCF of 9724 and 9728?

Answer:

Greatest Common Factor of 9724 and 9728 = 4

Step 1: Find the prime factorization of 9724

9724 = 2 x 2 x 11 x 13 x 17

Step 2: Find the prime factorization of 9728

9728 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 19

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 9724 and 9728 is 4