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, 1748 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1742 and 1748 is 2.
GCF(1742,1748) = 2
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 1748
2 | 1748 |
2 | 874 |
19 | 437 |
23 | 23 |
1 |
Prime factors of 1748 are 2,19,23. Prime factorization of 1748 in exponential form is:
1748 = 22×191×231
∴ So by taking common prime factors GCF of 1742 and 1748 is 2
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 1748
List of positive integer factors of 1748 that divides 1748 without a remainder.
1,2,4,19,23,38,46,76,92,437,874,1748
Greatest Common Factor
We found the factors and prime factorization of 1742 and 1748. The biggest common factor number is the GCF number.
So the greatest common factor 1742 and 1748 is 2.
Also check out the Least Common Multiple of 1742 and 1748
(i) The GCF of 1742 and 1748 is associative
GCF of 1742 and 1748 = GCF of 1748 and 1742
1. What is the GCF of 1742 and 1748?
Answer: GCF of 1742 and 1748 is 2.
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 1748?
Answer: Factors of 1748 are 1, 2, 4, 19, 23, 38, 46, 76, 92, 437, 874, 1748. There are 12 integers that are factors of 1748. The greatest factor of 1748 is 1748.
4. How to Find the GCF of 1742 and 1748?
Answer:
Greatest Common Factor of 1742 and 1748 = 2
Step 1: Find the prime factorization of 1742
1742 = 2 x 13 x 67
Step 2: Find the prime factorization of 1748
1748 = 2 x 2 x 19 x 23
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2
Step 4: Therefore, the greatest common factor of 1742 and 1748 is 2