GCF of 64/31, 686/27, 132/765
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 64/31, 686/27, 132/765 i.e 2/71145 easily. The following is the detailed procedure to determine the greatest common factor of fractions 64/31, 686/27, 132/765.
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 64/31,686/27,132/765?
Given fractions are 64/31,686/27,132/765
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 64/31,686/27,132/765, numerators are 64,686,132
Denominators are 31,27,765
The GCF of 64,686,132 is 2 .
LCM of 31,27,765 is 71145.
The greatest common factor of 64/31,686/27,132/765 = [GCF of 64,686,132]/[LCM of 31,27,765]= 2/71145
Therefore, the GCF of 64/31,686/27,132/765 is 2/71145.
To find the highest common factor of 64,686,132, we have to find the factors of both numbers and list the highest common factor.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The HCF of 64,686,132 is 2.
Lets's calculate GCF of 64,686,132
| 2 | 64, 686, 132 |
| 32, 343, 66 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 64,686,132 By Matching Biggest Common Factor Method
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 686
:1,2,7,14,49,98,343,686
Now, list down the factors of 132
:1,2,3,4,6,11,12,22,33,44,66,132
Greatest Common Factor
We found the factors 64,686,132 . The biggest common factor number is the GCF number.
So the greatest common factor 64,686,132 is 2.
Lets's calculate LCM of 31,27,765
| 3 | 31, 27, 765 |
| 3 | 31, 9, 255 |
| 31, 3, 85 |
∴ So the LCM of the given numbers is 3 x 3 x 31 x 3 x 85 = 71145
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/71145
Therefore, the GCF of Fractions 64/31,686/27,132/765 is 2/71145
Least Common Multiple of 31,27,765 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 31,27,765 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,27,765) = 1
common factors(in case of two or more numbers have common factors) = 9
GCF(31,27,765) x common factors =1 x 9 = 9
LCM(31,27,765) = ( 31 × 27 × 765 ) / 9
LCM(31,27,765) = 640305 / 9
LCM(31,27,765) = 71145
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FAQs on GCF of Fractions of 64/31, 686/27, 132/765
1. What is the HCF of 64,686,132?
The HCF of 64,686,132 is 2
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 64/31, 686/27, 132/765?
Answer: GCF of Numerators as per given numbers 64/31, 686/27, 132/765 is
GCF of Numerators i.e. for 64,686,132 is 2
LCM of denominators i.e. for 31,27,765 is 71145.
Thus, GCF of Fractions is 2/71145.Finally, GCF of Fractions for 64/31, 686/27, 132/765 is 2/71145.