Use our free GCF of Fractions Calculator tool to compute the GCF of 822/610, 138/708 i.e 6/215940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 822/610, 138/708.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 822/610,138/708
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 822/610,138/708, numerators are 822,138
Denominators are 610,708
The GCF of 822,138 is 6 .
LCM of 610,708 is 215940.
The greatest common factor of 822/610,138/708 = [GCF of 822,138]/[LCM of 610,708]= 6/215940
Therefore, the GCF of 822/610,138/708 is 6/215940.
To find the highest common factor of 822,138, we have to find the factors of both numbers and list the highest common factor.
The factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The HCF of 822,138 is 6.
Lets's calculate GCF of 822,138
2 | 822, 138 |
3 | 411, 69 |
137, 23 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 822
:1,2,3,6,137,274,411,822
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 822,138 . The biggest common factor number is the GCF number.
So the greatest common factor 822,138 is 6.
Lets's calculate LCM of 610,708
2 | 610, 708 |
305, 354 |
∴ So the LCM of the given numbers is 2 x 305 x 354 = 215940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/215940
Therefore, the GCF of Fractions 822/610,138/708 is 6/215940
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 610,708 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(610,708) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(610,708) x common factors =2 x 1 = 2
LCM(610,708) = ( 610 × 708 ) / 2
LCM(610,708) = 431880 / 2
LCM(610,708) = 215940
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 822,138?
The HCF of 822,138 is 6
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 822/610, 138/708?
Answer: GCF of Numerators as per given numbers 822/610, 138/708 is
GCF of Numerators i.e. for 822,138 is 6
LCM of denominators i.e. for 610,708 is 215940.
Thus, GCF of Fractions is 6/215940.Finally, GCF of Fractions for 822/610, 138/708 is 6/215940.