GCF of 85/87, 84/210, 191/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 85/87, 84/210, 191/420 i.e 1/12180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 85/87, 84/210, 191/420.
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 85/87,84/210,191/420?
Given fractions are 85/87,84/210,191/420
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 85/87,84/210,191/420, numerators are 85,84,191
Denominators are 87,210,420
The GCF of 85,84,191 is 1 .
LCM of 87,210,420 is 12180.
The greatest common factor of 85/87,84/210,191/420 = [GCF of 85,84,191]/[LCM of 87,210,420]= 1/12180
Therefore, the GCF of 85/87,84/210,191/420 is 1/12180.
To find the highest common factor of 85,84,191, we have to find the factors of both numbers and list the highest common factor.
The factors of 85 are 1, 5, 17, 85
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 191 are 1, 191
The HCF of 85,84,191 is 1.
Lets's calculate GCF of 85,84,191
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 85,84,191 By Matching Biggest Common Factor Method
Now, list down the factors of 85
:1,5,17,85
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 191
:1,191
Greatest Common Factor
We found the factors 85,84,191 . The biggest common factor number is the GCF number.
So the greatest common factor 85,84,191 is 1.
Lets's calculate LCM of 87,210,420
| 2 | 87, 210, 420 |
| 3 | 87, 105, 210 |
| 5 | 29, 35, 70 |
| 7 | 29, 7, 14 |
| 29, 1, 2 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 29 x 1 x 2 = 12180
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12180
Therefore, the GCF of Fractions 85/87,84/210,191/420 is 1/12180
Least Common Multiple of 87,210,420 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 87,210,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,210,420) = 3
common factors(in case of two or more numbers have common factors) = 210
GCF(87,210,420) x common factors =3 x 210 = 630
LCM(87,210,420) = ( 87 × 210 × 420 ) / 630
LCM(87,210,420) = 7673400 / 630
LCM(87,210,420) = 12180
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FAQs on GCF of Fractions of 85/87, 84/210, 191/420
1. What is the HCF of 85,84,191?
The HCF of 85,84,191 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 85/87, 84/210, 191/420?
Answer: GCF of Numerators as per given numbers 85/87, 84/210, 191/420 is
GCF of Numerators i.e. for 85,84,191 is 1
LCM of denominators i.e. for 87,210,420 is 12180.
Thus, GCF of Fractions is 1/12180.Finally, GCF of Fractions for 85/87, 84/210, 191/420 is 1/12180.