GCF of 854/105, 688/709
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 854/105, 688/709 i.e 2/74445 easily. The following is the detailed procedure to determine the greatest common factor of fractions 854/105, 688/709.
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 854/105,688/709?
Given fractions are 854/105,688/709
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 854/105,688/709, numerators are 854,688
Denominators are 105,709
The GCF of 854,688 is 2 .
LCM of 105,709 is 74445.
The greatest common factor of 854/105,688/709 = [GCF of 854,688]/[LCM of 105,709]= 2/74445
Therefore, the GCF of 854/105,688/709 is 2/74445.
To find the highest common factor of 854,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 854,688 is 2.
Lets's calculate GCF of 854,688
| 2 | 854, 688 |
| 427, 344 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 854,688 By Matching Biggest Common Factor Method
Now, list down the factors of 854
:1,2,7,14,61,122,427,854
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 854,688 . The biggest common factor number is the GCF number.
So the greatest common factor 854,688 is 2.
Lets's calculate LCM of 105,709
Given numbers has no common factors except 1. So, there LCM is their product i.e 74445
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/74445
Therefore, the GCF of Fractions 854/105,688/709 is 2/74445
Least Common Multiple of 105,709 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 105,709 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,709) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(105,709) x common factors =1 x 1 = 1
LCM(105,709) = ( 105 × 709 ) / 1
LCM(105,709) = 74445 / 1
LCM(105,709) = 74445
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 854/105, 688/709
1. What is the HCF of 854,688?
The HCF of 854,688 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 854/105, 688/709?
Answer: GCF of Numerators as per given numbers 854/105, 688/709 is
GCF of Numerators i.e. for 854,688 is 2
LCM of denominators i.e. for 105,709 is 74445.
Thus, GCF of Fractions is 2/74445.Finally, GCF of Fractions for 854/105, 688/709 is 2/74445.