GCF of 71/34, 297/84, 666/138
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 71/34, 297/84, 666/138 i.e 1/32844 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/34, 297/84, 666/138.
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 71/34,297/84,666/138?
Given fractions are 71/34,297/84,666/138
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 71/34,297/84,666/138, numerators are 71,297,666
Denominators are 34,84,138
The GCF of 71,297,666 is 1 .
LCM of 34,84,138 is 32844.
The greatest common factor of 71/34,297/84,666/138 = [GCF of 71,297,666]/[LCM of 34,84,138]= 1/32844
Therefore, the GCF of 71/34,297/84,666/138 is 1/32844.
To find the highest common factor of 71,297,666, we have to find the factors of both numbers and list the highest common factor.
The factors of 71 are 1, 71
The factors of 297 are 1, 3, 9, 11, 27, 33, 99, 297
The factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666
The HCF of 71,297,666 is 1.
Lets's calculate GCF of 71,297,666
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 71,297,666 By Matching Biggest Common Factor Method
Now, list down the factors of 71
:1,71
Now, list down the factors of 297
:1,3,9,11,27,33,99,297
Now, list down the factors of 666
:1,2,3,6,9,18,37,74,111,222,333,666
Greatest Common Factor
We found the factors 71,297,666 . The biggest common factor number is the GCF number.
So the greatest common factor 71,297,666 is 1.
Lets's calculate LCM of 34,84,138
| 2 | 34, 84, 138 |
| 3 | 17, 42, 69 |
| 17, 14, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 14 x 23 = 32844
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32844
Therefore, the GCF of Fractions 71/34,297/84,666/138 is 1/32844
Least Common Multiple of 34,84,138 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 34,84,138 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,84,138) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(34,84,138) x common factors =2 x 6 = 12
LCM(34,84,138) = ( 34 × 84 × 138 ) / 12
LCM(34,84,138) = 394128 / 12
LCM(34,84,138) = 32844
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FAQs on GCF of Fractions of 71/34, 297/84, 666/138
1. What is the HCF of 71,297,666?
The HCF of 71,297,666 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 71/34, 297/84, 666/138?
Answer: GCF of Numerators as per given numbers 71/34, 297/84, 666/138 is
GCF of Numerators i.e. for 71,297,666 is 1
LCM of denominators i.e. for 34,84,138 is 32844.
Thus, GCF of Fractions is 1/32844.Finally, GCF of Fractions for 71/34, 297/84, 666/138 is 1/32844.