Greatest Common Factor of 1728 and 1731

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, 1731 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1728 and 1731 is 3.

GCF(1728,1731) = 3

GCF of 1728 and 1731

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

GCF of:
and

Greatest Common Factor of 1728 and 1731

GCF of 1728 and 1731 is 3

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 1731


3 1731
577 577
1

Prime factors of 1731 are 3,577. Prime factorization of 1731 in exponential form is:

1731 = 31×5771

∴ So by taking common prime factors GCF of 1728 and 1731 is 3

Greatest Common Factor of 1728 and 1731 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 1731

List of positive integer factors of 1731 that divides 1731 without a remainder.

1,3,577,1731

Greatest Common Factor

We found the factors and prime factorization of 1728 and 1731. The biggest common factor number is the GCF number.
So the greatest common factor 1728 and 1731 is 3.

Also check out the Least Common Multiple of 1728 and 1731

Properties of GCF 1728 and 1731

(i) The GCF of 1728 and 1731 is associative

GCF of 1728 and 1731 = GCF of 1731 and 1728

Related Greatest Common Factor of 1728

Related Greatest Common Factor of 1731

Frequently Asked Questions on GCF of 1728 and 1731

1. What is the GCF of 1728 and 1731?

Answer: GCF of 1728 and 1731 is 3.

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 1731?

Answer: Factors of 1731 are 1, 3, 577, 1731. There are 4 integers that are factors of 1731. The greatest factor of 1731 is 1731.

4. How to Find the GCF of 1728 and 1731?

Answer:

Greatest Common Factor of 1728 and 1731 = 3

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 1731

1731 = 3 x 577

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 1728 and 1731 is 3