GCF of 266/84, 760/17, 742/57
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 266/84, 760/17, 742/57 i.e 2/27132 easily. The following is the detailed procedure to determine the greatest common factor of fractions 266/84, 760/17, 742/57.
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 266/84,760/17,742/57?
Given fractions are 266/84,760/17,742/57
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 266/84,760/17,742/57, numerators are 266,760,742
Denominators are 84,17,57
The GCF of 266,760,742 is 2 .
LCM of 84,17,57 is 27132.
The greatest common factor of 266/84,760/17,742/57 = [GCF of 266,760,742]/[LCM of 84,17,57]= 2/27132
Therefore, the GCF of 266/84,760/17,742/57 is 2/27132.
To find the highest common factor of 266,760,742, we have to find the factors of both numbers and list the highest common factor.
The factors of 266 are 1, 2, 7, 14, 19, 38, 133, 266
The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The HCF of 266,760,742 is 2.
Lets's calculate GCF of 266,760,742
| 2 | 266, 760, 742 |
| 133, 380, 371 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 266,760,742 By Matching Biggest Common Factor Method
Now, list down the factors of 266
:1,2,7,14,19,38,133,266
Now, list down the factors of 760
:1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Greatest Common Factor
We found the factors 266,760,742 . The biggest common factor number is the GCF number.
So the greatest common factor 266,760,742 is 2.
Lets's calculate LCM of 84,17,57
| 3 | 84, 17, 57 |
| 28, 17, 19 |
∴ So the LCM of the given numbers is 3 x 28 x 17 x 19 = 27132
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/27132
Therefore, the GCF of Fractions 266/84,760/17,742/57 is 2/27132
Least Common Multiple of 84,17,57 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 84,17,57 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,17,57) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(84,17,57) x common factors =1 x 3 = 3
LCM(84,17,57) = ( 84 × 17 × 57 ) / 3
LCM(84,17,57) = 81396 / 3
LCM(84,17,57) = 27132
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 266/84, 760/17, 742/57
1. What is the HCF of 266,760,742?
The HCF of 266,760,742 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 266/84, 760/17, 742/57?
Answer: GCF of Numerators as per given numbers 266/84, 760/17, 742/57 is
GCF of Numerators i.e. for 266,760,742 is 2
LCM of denominators i.e. for 84,17,57 is 27132.
Thus, GCF of Fractions is 2/27132.Finally, GCF of Fractions for 266/84, 760/17, 742/57 is 2/27132.