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 1742, 1749 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1742 and 1749 is 1.
GCF(1742,1749) = 1
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 1742
2 | 1742 |
13 | 871 |
67 | 67 |
1 |
Prime factors of 1742 are 2,13,67. Prime factorization of 1742 in exponential form is:
1742 = 21×131×671
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 1742 and 1749 is 1
Factors of 1742
List of positive integer factors of 1742 that divides 1742 without a remainder.
1,2,13,26,67,134,871,1742
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 1742 and 1749. The biggest common factor number is the GCF number.
So the greatest common factor 1742 and 1749 is 1.
Also check out the Least Common Multiple of 1742 and 1749
(i) The GCF of 1742 and 1749 is associative
GCF of 1742 and 1749 = GCF of 1749 and 1742
1. What is the GCF of 1742 and 1749?
Answer: GCF of 1742 and 1749 is 1.
2. What are the Factors of 1742?
Answer: Factors of 1742 are 1, 2, 13, 26, 67, 134, 871, 1742. There are 8 integers that are factors of 1742. The greatest factor of 1742 is 1742.
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 1742 and 1749?
Answer:
Greatest Common Factor of 1742 and 1749 = 1
Step 1: Find the prime factorization of 1742
1742 = 2 x 13 x 67
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 = = 1
Step 4: Therefore, the greatest common factor of 1742 and 1749 is 1