Greatest Common Factor of 1728 and 1729

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 1728, 1729 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1728 and 1729 is 1.

GCF(1728,1729) = 1

GCF of 1728 and 1729

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

GCF of:
and

Greatest Common Factor of 1728 and 1729

GCF of 1728 and 1729 is 1

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

Prime Factorization of 1729


7 1729
13 247
19 19
1

Prime factors of 1729 are 7,13,19. Prime factorization of 1729 in exponential form is:

1729 = 71×131×191

∴ So by taking common prime factors GCF of 1728 and 1729 is 1

Greatest Common Factor of 1728 and 1729 by matching factors method

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

Factors of 1729

List of positive integer factors of 1729 that divides 1729 without a remainder.

1,7,13,19,91,133,247,1729

Greatest Common Factor

We found the factors and prime factorization of 1728 and 1729. The biggest common factor number is the GCF number.
So the greatest common factor 1728 and 1729 is 1.

Also check out the Least Common Multiple of 1728 and 1729

Properties of GCF 1728 and 1729

(i) The GCF of 1728 and 1729 is associative

GCF of 1728 and 1729 = GCF of 1729 and 1728

Related Greatest Common Factor of 1728

Related Greatest Common Factor of 1729

Frequently Asked Questions on GCF of 1728 and 1729

1. What is the GCF of 1728 and 1729?

Answer: GCF of 1728 and 1729 is 1.

2. 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.

3. What are the Factors of 1729?

Answer: Factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729. There are 8 integers that are factors of 1729. The greatest factor of 1729 is 1729.

4. How to Find the GCF of 1728 and 1729?

Answer:

Greatest Common Factor of 1728 and 1729 = 1

Step 1: 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 2: Find the prime factorization of 1729

1729 = 7 x 13 x 19

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 1728 and 1729 is 1