GCF of 1742/657, 1840/7189
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1742/657, 1840/7189 i.e 2/4723173 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1742/657, 1840/7189.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 1742/657,1840/7189?
Given fractions are 1742/657,1840/7189
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 1742/657,1840/7189, numerators are 1742,1840
Denominators are 657,7189
The GCF of 1742,1840 is 2 .
LCM of 657,7189 is 4723173.
The greatest common factor of 1742/657,1840/7189 = [GCF of 1742,1840]/[LCM of 657,7189]= 2/4723173
Therefore, the GCF of 1742/657,1840/7189 is 2/4723173.
To find the highest common factor of 1742,1840, we have to find the factors of both numbers and list the highest common factor.
The factors of 1742 are 1, 2, 13, 26, 67, 134, 871, 1742
The factors of 1840 are 1, 2, 4, 5, 8, 10, 16, 20, 23, 40, 46, 80, 92, 115, 184, 230, 368, 460, 920, 1840
The HCF of 1742,1840 is 2.
Lets's calculate GCF of 1742,1840
| 2 | 1742, 1840 |
| 871, 920 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1742,1840 By Matching Biggest Common Factor Method
Now, list down the factors of 1742
:1,2,13,26,67,134,871,1742
Now, list down the factors of 1840
:1,2,4,5,8,10,16,20,23,40,46,80,92,115,184,230,368,460,920,1840
Greatest Common Factor
We found the factors 1742,1840 . The biggest common factor number is the GCF number.
So the greatest common factor 1742,1840 is 2.
Lets's calculate LCM of 657,7189
Given numbers has no common factors except 1. So, there LCM is their product i.e 4723173
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4723173
Therefore, the GCF of Fractions 1742/657,1840/7189 is 2/4723173
Least Common Multiple of 657,7189 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 657,7189 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(657,7189) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(657,7189) x common factors =1 x 1 = 1
LCM(657,7189) = ( 657 × 7189 ) / 1
LCM(657,7189) = 4723173 / 1
LCM(657,7189) = 4723173
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FAQs on GCF of Fractions of 1742/657, 1840/7189
1. What is the HCF of 1742,1840?
The HCF of 1742,1840 is 2
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 1742/657, 1840/7189?
Answer: GCF of Numerators as per given numbers 1742/657, 1840/7189 is
GCF of Numerators i.e. for 1742,1840 is 2
LCM of denominators i.e. for 657,7189 is 4723173.
Thus, GCF of Fractions is 2/4723173.Finally, GCF of Fractions for 1742/657, 1840/7189 is 2/4723173.