Use our free GCF of Fractions Calculator tool to compute the GCF of 87/84, 168/62, 719/678 i.e 1/294252 easily. The following is the detailed procedure to determine the greatest common factor of fractions 87/84, 168/62, 719/678.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 87/84,168/62,719/678
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 87/84,168/62,719/678, numerators are 87,168,719
Denominators are 84,62,678
The GCF of 87,168,719 is 1 .
LCM of 84,62,678 is 294252.
The greatest common factor of 87/84,168/62,719/678 = [GCF of 87,168,719]/[LCM of 84,62,678]= 1/294252
Therefore, the GCF of 87/84,168/62,719/678 is 1/294252.
To find the highest common factor of 87,168,719, we have to find the factors of both numbers and list the highest common factor.
The factors of 87 are 1, 3, 29, 87
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The factors of 719 are 1, 719
The HCF of 87,168,719 is 1.
Lets's calculate GCF of 87,168,719
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 87
:1,3,29,87
Now, list down the factors of 168
:1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Now, list down the factors of 719
:1,719
Greatest Common Factor
We found the factors 87,168,719 . The biggest common factor number is the GCF number.
So the greatest common factor 87,168,719 is 1.
Lets's calculate LCM of 84,62,678
2 | 84, 62, 678 |
3 | 42, 31, 339 |
14, 31, 113 |
∴ So the LCM of the given numbers is 2 x 3 x 14 x 31 x 113 = 294252
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/294252
Therefore, the GCF of Fractions 87/84,168/62,719/678 is 1/294252
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 84,62,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,62,678) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(84,62,678) x common factors =2 x 6 = 12
LCM(84,62,678) = ( 84 × 62 × 678 ) / 12
LCM(84,62,678) = 3531024 / 12
LCM(84,62,678) = 294252
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 87,168,719?
The HCF of 87,168,719 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 87/84, 168/62, 719/678?
Answer: GCF of Numerators as per given numbers 87/84, 168/62, 719/678 is
GCF of Numerators i.e. for 87,168,719 is 1
LCM of denominators i.e. for 84,62,678 is 294252.
Thus, GCF of Fractions is 1/294252.Finally, GCF of Fractions for 87/84, 168/62, 719/678 is 1/294252.