GCF of 7/20, 34/82, 15/258, 975/344
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7/20, 34/82, 15/258, 975/344 i.e 1/211560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7/20, 34/82, 15/258, 975/344.
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 7/20,34/82,15/258,975/344?
Given fractions are 7/20,34/82,15/258,975/344
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 7/20,34/82,15/258,975/344, numerators are 7,34,15,975
Denominators are 20,82,258,344
The GCF of 7,34,15,975 is 1 .
LCM of 20,82,258,344 is 211560.
The greatest common factor of 7/20,34/82,15/258,975/344 = [GCF of 7,34,15,975]/[LCM of 20,82,258,344]= 1/211560
Therefore, the GCF of 7/20,34/82,15/258,975/344 is 1/211560.
To find the highest common factor of 7,34,15,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 7 are 1, 7
The factors of 34 are 1, 2, 17, 34
The factors of 15 are 1, 3, 5, 15
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 7,34,15,975 is 1.
Lets's calculate GCF of 7,34,15,975
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7,34,15,975 By Matching Biggest Common Factor Method
Now, list down the factors of 7
:1,7
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 15
:1,3,5,15
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 7,34,15,975 . The biggest common factor number is the GCF number.
So the greatest common factor 7,34,15,975 is 1.
Lets's calculate LCM of 20,82,258,344
| 2 | 20, 82, 258, 344 |
| 2 | 10, 41, 129, 172 |
| 43 | 5, 41, 129, 86 |
| 5, 41, 3, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 43 x 5 x 41 x 3 x 2 = 211560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/211560
Therefore, the GCF of Fractions 7/20,34/82,15/258,975/344 is 1/211560
Least Common Multiple of 20,82,258,344 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 20,82,258,344 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,82,258,344) = 2
common factors(in case of two or more numbers have common factors) = 344
GCF(20,82,258,344) x common factors =2 x 344 = 688
LCM(20,82,258,344) = ( 20 × 82 × 258 × 344 ) / 688
LCM(20,82,258,344) = 145553280 / 688
LCM(20,82,258,344) = 211560
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 7/20, 34/82, 15/258, 975/344
1. What is the HCF of 7,34,15,975?
The HCF of 7,34,15,975 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 7/20, 34/82, 15/258, 975/344?
Answer: GCF of Numerators as per given numbers 7/20, 34/82, 15/258, 975/344 is
GCF of Numerators i.e. for 7,34,15,975 is 1
LCM of denominators i.e. for 20,82,258,344 is 211560.
Thus, GCF of Fractions is 1/211560.Finally, GCF of Fractions for 7/20, 34/82, 15/258, 975/344 is 1/211560.