Greatest Common Factor of 1722 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 1722, 1728 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1722 and 1728 is 6.

GCF(1722,1728) = 6

GCF of 1722 and 1728

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

GCF of:
and

Greatest Common Factor of 1722 and 1728

GCF of 1722 and 1728 is 6

Prime Factorization of 1722


2 1722
3 861
7 287
41 41
1

Prime factors of 1722 are 2,3,7,41. Prime factorization of 1722 in exponential form is:

1722 = 21×31×71×411

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 1722 and 1728 is 6

Greatest Common Factor of 1722 and 1728 by matching factors method

Factors of 1722

List of positive integer factors of 1722 that divides 1722 without a remainder.

1,2,3,6,7,14,21,41,42,82,123,246,287,574,861,1722

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 1722 and 1728. The biggest common factor number is the GCF number.
So the greatest common factor 1722 and 1728 is 6.

Also check out the Least Common Multiple of 1722 and 1728

Properties of GCF 1722 and 1728

(i) The GCF of 1722 and 1728 is associative

GCF of 1722 and 1728 = GCF of 1728 and 1722

Related Greatest Common Factor of 1722

Related Greatest Common Factor of 1728

Frequently Asked Questions on GCF of 1722 and 1728

1. What is the GCF of 1722 and 1728?

Answer: GCF of 1722 and 1728 is 6.

2. What are the Factors of 1722?

Answer: Factors of 1722 are 1, 2, 3, 6, 7, 14, 21, 41, 42, 82, 123, 246, 287, 574, 861, 1722. There are 16 integers that are factors of 1722. The greatest factor of 1722 is 1722.

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 1722 and 1728?

Answer:

Greatest Common Factor of 1722 and 1728 = 6

Step 1: Find the prime factorization of 1722

1722 = 2 x 3 x 7 x 41

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 3 = 6

Step 4: Therefore, the greatest common factor of 1722 and 1728 is 6