GCF of 710/765, 731/685
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 710/765, 731/685 i.e 1/104805 easily. The following is the detailed procedure to determine the greatest common factor of fractions 710/765, 731/685.
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 710/765,731/685?
Given fractions are 710/765,731/685
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 710/765,731/685, numerators are 710,731
Denominators are 765,685
The GCF of 710,731 is 1 .
LCM of 765,685 is 104805.
The greatest common factor of 710/765,731/685 = [GCF of 710,731]/[LCM of 765,685]= 1/104805
Therefore, the GCF of 710/765,731/685 is 1/104805.
To find the highest common factor of 710,731, we have to find the factors of both numbers and list the highest common factor.
The factors of 710 are 1, 2, 5, 10, 71, 142, 355, 710
The factors of 731 are 1, 17, 43, 731
The HCF of 710,731 is 1.
Lets's calculate GCF of 710,731
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 710,731 By Matching Biggest Common Factor Method
Now, list down the factors of 710
:1,2,5,10,71,142,355,710
Now, list down the factors of 731
:1,17,43,731
Greatest Common Factor
We found the factors 710,731 . The biggest common factor number is the GCF number.
So the greatest common factor 710,731 is 1.
Lets's calculate LCM of 765,685
| 5 | 765, 685 |
| 153, 137 |
∴ So the LCM of the given numbers is 5 x 153 x 137 = 104805
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/104805
Therefore, the GCF of Fractions 710/765,731/685 is 1/104805
Least Common Multiple of 765,685 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 765,685 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(765,685) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(765,685) x common factors =5 x 1 = 5
LCM(765,685) = ( 765 × 685 ) / 5
LCM(765,685) = 524025 / 5
LCM(765,685) = 104805
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FAQs on GCF of Fractions of 710/765, 731/685
1. What is the HCF of 710,731?
The HCF of 710,731 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 710/765, 731/685?
Answer: GCF of Numerators as per given numbers 710/765, 731/685 is
GCF of Numerators i.e. for 710,731 is 1
LCM of denominators i.e. for 765,685 is 104805.
Thus, GCF of Fractions is 1/104805.Finally, GCF of Fractions for 710/765, 731/685 is 1/104805.