Greatest Common Factor of 1720 and 1728

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 1720, 1728 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1720 and 1728 is 8.

GCF(1720,1728) = 8

GCF of 1720 and 1728

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

GCF of:
and

Greatest Common Factor of 1720 and 1728

GCF of 1720 and 1728 is 8

Prime Factorization of 1720


2 1720
2 860
2 430
5 215
43 43
1

Prime factors of 1720 are 2,5,43. Prime factorization of 1720 in exponential form is:

1720 = 23×51×431

Prime Factorization of 1728


2 1728
2 864
2 432
2 216
2 108
2 54
3 27
3 9
3 3
1

Prime factors of 1728 are 2,3. Prime factorization of 1728 in exponential form is:

1728 = 26×33

∴ So by taking common prime factors GCF of 1720 and 1728 is 8

Greatest Common Factor of 1720 and 1728 by matching factors method

Factors of 1720

List of positive integer factors of 1720 that divides 1720 without a remainder.

1,2,4,5,8,10,20,40,43,86,172,215,344,430,860,1720

Factors of 1728

List of positive integer factors of 1728 that divides 1728 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,64,72,96,108,144,192,216,288,432,576,864,1728

Greatest Common Factor

We found the factors and prime factorization of 1720 and 1728. The biggest common factor number is the GCF number.
So the greatest common factor 1720 and 1728 is 8.

Also check out the Least Common Multiple of 1720 and 1728

Properties of GCF 1720 and 1728

(i) The GCF of 1720 and 1728 is associative

GCF of 1720 and 1728 = GCF of 1728 and 1720

Related Greatest Common Factor of 1720

Related Greatest Common Factor of 1728

Frequently Asked Questions on GCF of 1720 and 1728

1. What is the GCF of 1720 and 1728?

Answer: GCF of 1720 and 1728 is 8.

2. What are the Factors of 1720?

Answer: Factors of 1720 are 1, 2, 4, 5, 8, 10, 20, 40, 43, 86, 172, 215, 344, 430, 860, 1720. There are 16 integers that are factors of 1720. The greatest factor of 1720 is 1720.

3. What are the Factors of 1728?

Answer: Factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728. There are 28 integers that are factors of 1728. The greatest factor of 1728 is 1728.

4. How to Find the GCF of 1720 and 1728?

Answer:

Greatest Common Factor of 1720 and 1728 = 8

Step 1: Find the prime factorization of 1720

1720 = 2 x 2 x 2 x 5 x 43

Step 2: Find the prime factorization of 1728

1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

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

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 1720 and 1728 is 8