Use our free GCF of Fractions Calculator tool to compute the GCF of 84/60, 711/39, 821/106 i.e 1/41340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 84/60, 711/39, 821/106.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 84/60,711/39,821/106
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 84/60,711/39,821/106, numerators are 84,711,821
Denominators are 60,39,106
The GCF of 84,711,821 is 1 .
LCM of 60,39,106 is 41340.
The greatest common factor of 84/60,711/39,821/106 = [GCF of 84,711,821]/[LCM of 60,39,106]= 1/41340
Therefore, the GCF of 84/60,711/39,821/106 is 1/41340.
To find the highest common factor of 84,711,821, we have to find the factors of both numbers and list the highest common factor.
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 711 are 1, 3, 9, 79, 237, 711
The factors of 821 are 1, 821
The HCF of 84,711,821 is 1.
Lets's calculate GCF of 84,711,821
∴ So GCF of numbers is 1 because of no common factors present between them.
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 711
:1,3,9,79,237,711
Now, list down the factors of 821
:1,821
Greatest Common Factor
We found the factors 84,711,821 . The biggest common factor number is the GCF number.
So the greatest common factor 84,711,821 is 1.
Lets's calculate LCM of 60,39,106
2 | 60, 39, 106 |
3 | 30, 39, 53 |
10, 13, 53 |
∴ So the LCM of the given numbers is 2 x 3 x 10 x 13 x 53 = 41340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/41340
Therefore, the GCF of Fractions 84/60,711/39,821/106 is 1/41340
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 60,39,106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,39,106) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(60,39,106) x common factors =1 x 6 = 6
LCM(60,39,106) = ( 60 × 39 × 106 ) / 6
LCM(60,39,106) = 248040 / 6
LCM(60,39,106) = 41340
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 84,711,821?
The HCF of 84,711,821 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 84/60, 711/39, 821/106?
Answer: GCF of Numerators as per given numbers 84/60, 711/39, 821/106 is
GCF of Numerators i.e. for 84,711,821 is 1
LCM of denominators i.e. for 60,39,106 is 41340.
Thus, GCF of Fractions is 1/41340.Finally, GCF of Fractions for 84/60, 711/39, 821/106 is 1/41340.