Greatest Common Factor of 1728 and 1732

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, 1732 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1728 and 1732 is 4.

GCF(1728,1732) = 4

GCF of 1728 and 1732

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

GCF of:
and

Greatest Common Factor of 1728 and 1732

GCF of 1728 and 1732 is 4

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 1732


2 1732
2 866
433 433
1

Prime factors of 1732 are 2,433. Prime factorization of 1732 in exponential form is:

1732 = 22×4331

∴ So by taking common prime factors GCF of 1728 and 1732 is 4

Greatest Common Factor of 1728 and 1732 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 1732

List of positive integer factors of 1732 that divides 1732 without a remainder.

1,2,4,433,866,1732

Greatest Common Factor

We found the factors and prime factorization of 1728 and 1732. The biggest common factor number is the GCF number.
So the greatest common factor 1728 and 1732 is 4.

Also check out the Least Common Multiple of 1728 and 1732

Properties of GCF 1728 and 1732

(i) The GCF of 1728 and 1732 is associative

GCF of 1728 and 1732 = GCF of 1732 and 1728

Related Greatest Common Factor of 1728

Related Greatest Common Factor of 1732

Frequently Asked Questions on GCF of 1728 and 1732

1. What is the GCF of 1728 and 1732?

Answer: GCF of 1728 and 1732 is 4.

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 1732?

Answer: Factors of 1732 are 1, 2, 4, 433, 866, 1732. There are 6 integers that are factors of 1732. The greatest factor of 1732 is 1732.

4. How to Find the GCF of 1728 and 1732?

Answer:

Greatest Common Factor of 1728 and 1732 = 4

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 1732

1732 = 2 x 2 x 433

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 1728 and 1732 is 4