GCF of 86/420, 99/560, 709/660
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 86/420, 99/560, 709/660 i.e 1/18480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/420, 99/560, 709/660.
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 86/420,99/560,709/660?
Given fractions are 86/420,99/560,709/660
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 86/420,99/560,709/660, numerators are 86,99,709
Denominators are 420,560,660
The GCF of 86,99,709 is 1 .
LCM of 420,560,660 is 18480.
The greatest common factor of 86/420,99/560,709/660 = [GCF of 86,99,709]/[LCM of 420,560,660]= 1/18480
Therefore, the GCF of 86/420,99/560,709/660 is 1/18480.
To find the highest common factor of 86,99,709, we have to find the factors of both numbers and list the highest common factor.
The factors of 86 are 1, 2, 43, 86
The factors of 99 are 1, 3, 9, 11, 33, 99
The factors of 709 are 1, 709
The HCF of 86,99,709 is 1.
Lets's calculate GCF of 86,99,709
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 86,99,709 By Matching Biggest Common Factor Method
Now, list down the factors of 86
:1,2,43,86
Now, list down the factors of 99
:1,3,9,11,33,99
Now, list down the factors of 709
:1,709
Greatest Common Factor
We found the factors 86,99,709 . The biggest common factor number is the GCF number.
So the greatest common factor 86,99,709 is 1.
Lets's calculate LCM of 420,560,660
| 2 | 420, 560, 660 |
| 2 | 210, 280, 330 |
| 3 | 105, 140, 165 |
| 5 | 35, 140, 55 |
| 7 | 7, 28, 11 |
| 1, 4, 11 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 7 x 1 x 4 x 11 = 18480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18480
Therefore, the GCF of Fractions 86/420,99/560,709/660 is 1/18480
Least Common Multiple of 420,560,660 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 420,560,660 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,560,660) = 20
common factors(in case of two or more numbers have common factors) = 420
GCF(420,560,660) x common factors =20 x 420 = 8400
LCM(420,560,660) = ( 420 × 560 × 660 ) / 8400
LCM(420,560,660) = 155232000 / 8400
LCM(420,560,660) = 18480
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FAQs on GCF of Fractions of 86/420, 99/560, 709/660
1. What is the HCF of 86,99,709?
The HCF of 86,99,709 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 86/420, 99/560, 709/660?
Answer: GCF of Numerators as per given numbers 86/420, 99/560, 709/660 is
GCF of Numerators i.e. for 86,99,709 is 1
LCM of denominators i.e. for 420,560,660 is 18480.
Thus, GCF of Fractions is 1/18480.Finally, GCF of Fractions for 86/420, 99/560, 709/660 is 1/18480.