Use our free GCF of Fractions Calculator tool to compute the GCF of 353/658, 686/141 i.e 1/1974 easily. The following is the detailed procedure to determine the greatest common factor of fractions 353/658, 686/141.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 353/658,686/141
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 353/658,686/141, numerators are 353,686
Denominators are 658,141
The GCF of 353,686 is 1 .
LCM of 658,141 is 1974.
The greatest common factor of 353/658,686/141 = [GCF of 353,686]/[LCM of 658,141]= 1/1974
Therefore, the GCF of 353/658,686/141 is 1/1974.
To find the highest common factor of 353,686, we have to find the factors of both numbers and list the highest common factor.
The factors of 353 are 1, 353
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686
The HCF of 353,686 is 1.
Lets's calculate GCF of 353,686
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 353
:1,353
Now, list down the factors of 686
:1,2,7,14,49,98,343,686
Greatest Common Factor
We found the factors 353,686 . The biggest common factor number is the GCF number.
So the greatest common factor 353,686 is 1.
Lets's calculate LCM of 658,141
47 | 658, 141 |
14, 3 |
∴ So the LCM of the given numbers is 47 x 14 x 3 = 1974
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1974
Therefore, the GCF of Fractions 353/658,686/141 is 1/1974
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 658,141 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(658,141) = 47
common factors(in case of two or more numbers have common factors) = 1
GCF(658,141) x common factors =47 x 1 = 47
LCM(658,141) = ( 658 × 141 ) / 47
LCM(658,141) = 92778 / 47
LCM(658,141) = 1974
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 353,686?
The HCF of 353,686 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 353/658, 686/141?
Answer: GCF of Numerators as per given numbers 353/658, 686/141 is
GCF of Numerators i.e. for 353,686 is 1
LCM of denominators i.e. for 658,141 is 1974.
Thus, GCF of Fractions is 1/1974.Finally, GCF of Fractions for 353/658, 686/141 is 1/1974.