GCF of 14/71, 96/29, 87/87, 89/840
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 14/71, 96/29, 87/87, 89/840 i.e 1/1729560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/71, 96/29, 87/87, 89/840.
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 14/71,96/29,87/87,89/840?
Given fractions are 14/71,96/29,87/87,89/840
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 14/71,96/29,87/87,89/840, numerators are 14,96,87,89
Denominators are 71,29,87,840
The GCF of 14,96,87,89 is 1 .
LCM of 71,29,87,840 is 1729560.
The greatest common factor of 14/71,96/29,87/87,89/840 = [GCF of 14,96,87,89]/[LCM of 71,29,87,840]= 1/1729560
Therefore, the GCF of 14/71,96/29,87/87,89/840 is 1/1729560.
To find the highest common factor of 14,96,87,89, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 87 are 1, 3, 29, 87
The factors of 89 are 1, 89
The HCF of 14,96,87,89 is 1.
Lets's calculate GCF of 14,96,87,89
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 14,96,87,89 By Matching Biggest Common Factor Method
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 87
:1,3,29,87
Now, list down the factors of 89
:1,89
Greatest Common Factor
We found the factors 14,96,87,89 . The biggest common factor number is the GCF number.
So the greatest common factor 14,96,87,89 is 1.
Lets's calculate LCM of 71,29,87,840
| 3 | 71, 29, 87, 840 |
| 29 | 71, 29, 29, 280 |
| 71, 1, 1, 280 |
∴ So the LCM of the given numbers is 3 x 29 x 71 x 1 x 1 x 280 = 1729560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1729560
Therefore, the GCF of Fractions 14/71,96/29,87/87,89/840 is 1/1729560
Least Common Multiple of 71,29,87,840 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 71,29,87,840 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,29,87,840) = 1
common factors(in case of two or more numbers have common factors) = 87
GCF(71,29,87,840) x common factors =1 x 87 = 87
LCM(71,29,87,840) = ( 71 × 29 × 87 × 840 ) / 87
LCM(71,29,87,840) = 150471720 / 87
LCM(71,29,87,840) = 1729560
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 14/71, 96/29, 87/87, 89/840
1. What is the HCF of 14,96,87,89?
The HCF of 14,96,87,89 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 14/71, 96/29, 87/87, 89/840?
Answer: GCF of Numerators as per given numbers 14/71, 96/29, 87/87, 89/840 is
GCF of Numerators i.e. for 14,96,87,89 is 1
LCM of denominators i.e. for 71,29,87,840 is 1729560.
Thus, GCF of Fractions is 1/1729560.Finally, GCF of Fractions for 14/71, 96/29, 87/87, 89/840 is 1/1729560.