GCF of 706/85, 419/810
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 706/85, 419/810 i.e 1/13770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 706/85, 419/810.
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 706/85,419/810?
Given fractions are 706/85,419/810
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 706/85,419/810, numerators are 706,419
Denominators are 85,810
The GCF of 706,419 is 1 .
LCM of 85,810 is 13770.
The greatest common factor of 706/85,419/810 = [GCF of 706,419]/[LCM of 85,810]= 1/13770
Therefore, the GCF of 706/85,419/810 is 1/13770.
To find the highest common factor of 706,419, we have to find the factors of both numbers and list the highest common factor.
The factors of 706 are 1, 2, 353, 706
The factors of 419 are 1, 419
The HCF of 706,419 is 1.
Lets's calculate GCF of 706,419
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 706,419 By Matching Biggest Common Factor Method
Now, list down the factors of 706
:1,2,353,706
Now, list down the factors of 419
:1,419
Greatest Common Factor
We found the factors 706,419 . The biggest common factor number is the GCF number.
So the greatest common factor 706,419 is 1.
Lets's calculate LCM of 85,810
| 5 | 85, 810 |
| 17, 162 |
∴ So the LCM of the given numbers is 5 x 17 x 162 = 13770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13770
Therefore, the GCF of Fractions 706/85,419/810 is 1/13770
Least Common Multiple of 85,810 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 85,810 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,810) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(85,810) x common factors =5 x 1 = 5
LCM(85,810) = ( 85 × 810 ) / 5
LCM(85,810) = 68850 / 5
LCM(85,810) = 13770
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 706/85, 419/810
1. What is the HCF of 706,419?
The HCF of 706,419 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 706/85, 419/810?
Answer: GCF of Numerators as per given numbers 706/85, 419/810 is
GCF of Numerators i.e. for 706,419 is 1
LCM of denominators i.e. for 85,810 is 13770.
Thus, GCF of Fractions is 1/13770.Finally, GCF of Fractions for 706/85, 419/810 is 1/13770.