GCF of 87/34, 822/27, 945/154
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 87/34, 822/27, 945/154 i.e 3/70686 easily. The following is the detailed procedure to determine the greatest common factor of fractions 87/34, 822/27, 945/154.
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 87/34,822/27,945/154?
Given fractions are 87/34,822/27,945/154
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 87/34,822/27,945/154, numerators are 87,822,945
Denominators are 34,27,154
The GCF of 87,822,945 is 3 .
LCM of 34,27,154 is 70686.
The greatest common factor of 87/34,822/27,945/154 = [GCF of 87,822,945]/[LCM of 34,27,154]= 3/70686
Therefore, the GCF of 87/34,822/27,945/154 is 3/70686.
To find the highest common factor of 87,822,945, 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 822 are 1, 2, 3, 6, 137, 274, 411, 822
The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945
The HCF of 87,822,945 is 3.
Lets's calculate GCF of 87,822,945
| 3 | 87, 822, 945 |
| 29, 274, 315 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 87,822,945 By Matching Biggest Common Factor Method
Now, list down the factors of 87
:1,3,29,87
Now, list down the factors of 822
:1,2,3,6,137,274,411,822
Now, list down the factors of 945
:1,3,5,7,9,15,21,27,35,45,63,105,135,189,315,945
Greatest Common Factor
We found the factors 87,822,945 . The biggest common factor number is the GCF number.
So the greatest common factor 87,822,945 is 3.
Lets's calculate LCM of 34,27,154
| 2 | 34, 27, 154 |
| 17, 27, 77 |
∴ So the LCM of the given numbers is 2 x 17 x 27 x 77 = 70686
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/70686
Therefore, the GCF of Fractions 87/34,822/27,945/154 is 3/70686
Least Common Multiple of 34,27,154 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 34,27,154 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,27,154) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(34,27,154) x common factors =1 x 2 = 2
LCM(34,27,154) = ( 34 × 27 × 154 ) / 2
LCM(34,27,154) = 141372 / 2
LCM(34,27,154) = 70686
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 87/34, 822/27, 945/154
1. What is the HCF of 87,822,945?
The HCF of 87,822,945 is 3
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 87/34, 822/27, 945/154?
Answer: GCF of Numerators as per given numbers 87/34, 822/27, 945/154 is
GCF of Numerators i.e. for 87,822,945 is 3
LCM of denominators i.e. for 34,27,154 is 70686.
Thus, GCF of Fractions is 3/70686.Finally, GCF of Fractions for 87/34, 822/27, 945/154 is 3/70686.