Greatest Common Factor of 1746 and 1749

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 1746, 1749 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1746 and 1749 is 3.

GCF(1746,1749) = 3

GCF of 1746 and 1749

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

GCF of:
and

Greatest Common Factor of 1746 and 1749

GCF of 1746 and 1749 is 3

Prime Factorization of 1746


2 1746
3 873
3 291
97 97
1

Prime factors of 1746 are 2,3,97. Prime factorization of 1746 in exponential form is:

1746 = 21×32×971

Prime Factorization of 1749


3 1749
11 583
53 53
1

Prime factors of 1749 are 3,11,53. Prime factorization of 1749 in exponential form is:

1749 = 31×111×531

∴ So by taking common prime factors GCF of 1746 and 1749 is 3

Greatest Common Factor of 1746 and 1749 by matching factors method

Factors of 1746

List of positive integer factors of 1746 that divides 1746 without a remainder.

1,2,3,6,9,18,97,194,291,582,873,1746

Factors of 1749

List of positive integer factors of 1749 that divides 1749 without a remainder.

1,3,11,33,53,159,583,1749

Greatest Common Factor

We found the factors and prime factorization of 1746 and 1749. The biggest common factor number is the GCF number.
So the greatest common factor 1746 and 1749 is 3.

Also check out the Least Common Multiple of 1746 and 1749

Properties of GCF 1746 and 1749

(i) The GCF of 1746 and 1749 is associative

GCF of 1746 and 1749 = GCF of 1749 and 1746

Related Greatest Common Factor of 1746

Related Greatest Common Factor of 1749

Frequently Asked Questions on GCF of 1746 and 1749

1. What is the GCF of 1746 and 1749?

Answer: GCF of 1746 and 1749 is 3.

2. What are the Factors of 1746?

Answer: Factors of 1746 are 1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873, 1746. There are 12 integers that are factors of 1746. The greatest factor of 1746 is 1746.

3. What are the Factors of 1749?

Answer: Factors of 1749 are 1, 3, 11, 33, 53, 159, 583, 1749. There are 8 integers that are factors of 1749. The greatest factor of 1749 is 1749.

4. How to Find the GCF of 1746 and 1749?

Answer:

Greatest Common Factor of 1746 and 1749 = 3

Step 1: Find the prime factorization of 1746

1746 = 2 x 3 x 3 x 97

Step 2: Find the prime factorization of 1749

1749 = 3 x 11 x 53

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 1746 and 1749 is 3