GCF of 654/685, 4114/315
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 654/685, 4114/315 i.e 2/43155 easily. The following is the detailed procedure to determine the greatest common factor of fractions 654/685, 4114/315.
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 654/685,4114/315?
Given fractions are 654/685,4114/315
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 654/685,4114/315, numerators are 654,4114
Denominators are 685,315
The GCF of 654,4114 is 2 .
LCM of 685,315 is 43155.
The greatest common factor of 654/685,4114/315 = [GCF of 654,4114]/[LCM of 685,315]= 2/43155
Therefore, the GCF of 654/685,4114/315 is 2/43155.
To find the highest common factor of 654,4114, we have to find the factors of both numbers and list the highest common factor.
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The factors of 4114 are 1, 2, 11, 17, 22, 34, 121, 187, 242, 374, 2057, 4114
The HCF of 654,4114 is 2.
Lets's calculate GCF of 654,4114
| 2 | 654, 4114 |
| 327, 2057 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 654,4114 By Matching Biggest Common Factor Method
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Now, list down the factors of 4114
:1,2,11,17,22,34,121,187,242,374,2057,4114
Greatest Common Factor
We found the factors 654,4114 . The biggest common factor number is the GCF number.
So the greatest common factor 654,4114 is 2.
Lets's calculate LCM of 685,315
| 5 | 685, 315 |
| 137, 63 |
∴ So the LCM of the given numbers is 5 x 137 x 63 = 43155
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/43155
Therefore, the GCF of Fractions 654/685,4114/315 is 2/43155
Least Common Multiple of 685,315 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 685,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(685,315) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(685,315) x common factors =5 x 1 = 5
LCM(685,315) = ( 685 × 315 ) / 5
LCM(685,315) = 215775 / 5
LCM(685,315) = 43155
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 654/685, 4114/315
1. What is the HCF of 654,4114?
The HCF of 654,4114 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 654/685, 4114/315?
Answer: GCF of Numerators as per given numbers 654/685, 4114/315 is
GCF of Numerators i.e. for 654,4114 is 2
LCM of denominators i.e. for 685,315 is 43155.
Thus, GCF of Fractions is 2/43155.Finally, GCF of Fractions for 654/685, 4114/315 is 2/43155.