GCF of 991/34, 709/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 991/34, 709/678 i.e 1/11526 easily. The following is the detailed procedure to determine the greatest common factor of fractions 991/34, 709/678.
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 991/34,709/678?
Given fractions are 991/34,709/678
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 991/34,709/678, numerators are 991,709
Denominators are 34,678
The GCF of 991,709 is 1 .
LCM of 34,678 is 11526.
The greatest common factor of 991/34,709/678 = [GCF of 991,709]/[LCM of 34,678]= 1/11526
Therefore, the GCF of 991/34,709/678 is 1/11526.
To find the highest common factor of 991,709, we have to find the factors of both numbers and list the highest common factor.
The factors of 991 are 1, 991
The factors of 709 are 1, 709
The HCF of 991,709 is 1.
Lets's calculate GCF of 991,709
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 991,709 By Matching Biggest Common Factor Method
Now, list down the factors of 991
:1,991
Now, list down the factors of 709
:1,709
Greatest Common Factor
We found the factors 991,709 . The biggest common factor number is the GCF number.
So the greatest common factor 991,709 is 1.
Lets's calculate LCM of 34,678
| 2 | 34, 678 |
| 17, 339 |
∴ So the LCM of the given numbers is 2 x 17 x 339 = 11526
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11526
Therefore, the GCF of Fractions 991/34,709/678 is 1/11526
Least Common Multiple of 34,678 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 34,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,678) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,678) x common factors =2 x 1 = 2
LCM(34,678) = ( 34 × 678 ) / 2
LCM(34,678) = 23052 / 2
LCM(34,678) = 11526
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FAQs on GCF of Fractions of 991/34, 709/678
1. What is the HCF of 991,709?
The HCF of 991,709 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 991/34, 709/678?
Answer: GCF of Numerators as per given numbers 991/34, 709/678 is
GCF of Numerators i.e. for 991,709 is 1
LCM of denominators i.e. for 34,678 is 11526.
Thus, GCF of Fractions is 1/11526.Finally, GCF of Fractions for 991/34, 709/678 is 1/11526.