GCF of 3705/842, 1642/7154
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3705/842, 1642/7154 i.e 1/3011834 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3705/842, 1642/7154.
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 3705/842,1642/7154?
Given fractions are 3705/842,1642/7154
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 3705/842,1642/7154, numerators are 3705,1642
Denominators are 842,7154
The GCF of 3705,1642 is 1 .
LCM of 842,7154 is 3011834.
The greatest common factor of 3705/842,1642/7154 = [GCF of 3705,1642]/[LCM of 842,7154]= 1/3011834
Therefore, the GCF of 3705/842,1642/7154 is 1/3011834.
To find the highest common factor of 3705,1642, we have to find the factors of both numbers and list the highest common factor.
The factors of 3705 are 1, 3, 5, 13, 15, 19, 39, 57, 65, 95, 195, 247, 285, 741, 1235, 3705
The factors of 1642 are 1, 2, 821, 1642
The HCF of 3705,1642 is 1.
Lets's calculate GCF of 3705,1642
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3705,1642 By Matching Biggest Common Factor Method
Now, list down the factors of 3705
:1,3,5,13,15,19,39,57,65,95,195,247,285,741,1235,3705
Now, list down the factors of 1642
:1,2,821,1642
Greatest Common Factor
We found the factors 3705,1642 . The biggest common factor number is the GCF number.
So the greatest common factor 3705,1642 is 1.
Lets's calculate LCM of 842,7154
| 2 | 842, 7154 |
| 421, 3577 |
∴ So the LCM of the given numbers is 2 x 421 x 3577 = 3011834
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3011834
Therefore, the GCF of Fractions 3705/842,1642/7154 is 1/3011834
Least Common Multiple of 842,7154 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 842,7154 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(842,7154) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(842,7154) x common factors =2 x 1 = 2
LCM(842,7154) = ( 842 × 7154 ) / 2
LCM(842,7154) = 6023668 / 2
LCM(842,7154) = 3011834
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FAQs on GCF of Fractions of 3705/842, 1642/7154
1. What is the HCF of 3705,1642?
The HCF of 3705,1642 is 1
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 3705/842, 1642/7154?
Answer: GCF of Numerators as per given numbers 3705/842, 1642/7154 is
GCF of Numerators i.e. for 3705,1642 is 1
LCM of denominators i.e. for 842,7154 is 3011834.
Thus, GCF of Fractions is 1/3011834.Finally, GCF of Fractions for 3705/842, 1642/7154 is 1/3011834.