GCF of 711/78, 202/22, 413/66
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 711/78, 202/22, 413/66 i.e 1/858 easily. The following is the detailed procedure to determine the greatest common factor of fractions 711/78, 202/22, 413/66.
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 711/78,202/22,413/66?
Given fractions are 711/78,202/22,413/66
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 711/78,202/22,413/66, numerators are 711,202,413
Denominators are 78,22,66
The GCF of 711,202,413 is 1 .
LCM of 78,22,66 is 858.
The greatest common factor of 711/78,202/22,413/66 = [GCF of 711,202,413]/[LCM of 78,22,66]= 1/858
Therefore, the GCF of 711/78,202/22,413/66 is 1/858.
To find the highest common factor of 711,202,413, we have to find the factors of both numbers and list the highest common factor.
The factors of 711 are 1, 3, 9, 79, 237, 711
The factors of 202 are 1, 2, 101, 202
The factors of 413 are 1, 7, 59, 413
The HCF of 711,202,413 is 1.
Lets's calculate GCF of 711,202,413
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 711,202,413 By Matching Biggest Common Factor Method
Now, list down the factors of 711
:1,3,9,79,237,711
Now, list down the factors of 202
:1,2,101,202
Now, list down the factors of 413
:1,7,59,413
Greatest Common Factor
We found the factors 711,202,413 . The biggest common factor number is the GCF number.
So the greatest common factor 711,202,413 is 1.
Lets's calculate LCM of 78,22,66
| 2 | 78, 22, 66 |
| 3 | 39, 11, 33 |
| 11 | 13, 11, 11 |
| 13, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 11 x 13 x 1 x 1 = 858
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/858
Therefore, the GCF of Fractions 711/78,202/22,413/66 is 1/858
Least Common Multiple of 78,22,66 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 78,22,66 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,22,66) = 2
common factors(in case of two or more numbers have common factors) = 66
GCF(78,22,66) x common factors =2 x 66 = 132
LCM(78,22,66) = ( 78 × 22 × 66 ) / 132
LCM(78,22,66) = 113256 / 132
LCM(78,22,66) = 858
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FAQs on GCF of Fractions of 711/78, 202/22, 413/66
1. What is the HCF of 711,202,413?
The HCF of 711,202,413 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 711/78, 202/22, 413/66?
Answer: GCF of Numerators as per given numbers 711/78, 202/22, 413/66 is
GCF of Numerators i.e. for 711,202,413 is 1
LCM of denominators i.e. for 78,22,66 is 858.
Thus, GCF of Fractions is 1/858.Finally, GCF of Fractions for 711/78, 202/22, 413/66 is 1/858.