GCF of 86/77, 360/52, 108/208
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 86/77, 360/52, 108/208 i.e 2/16016 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/77, 360/52, 108/208.
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 86/77,360/52,108/208?
Given fractions are 86/77,360/52,108/208
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 86/77,360/52,108/208, numerators are 86,360,108
Denominators are 77,52,208
The GCF of 86,360,108 is 2 .
LCM of 77,52,208 is 16016.
The greatest common factor of 86/77,360/52,108/208 = [GCF of 86,360,108]/[LCM of 77,52,208]= 2/16016
Therefore, the GCF of 86/77,360/52,108/208 is 2/16016.
To find the highest common factor of 86,360,108, we have to find the factors of both numbers and list the highest common factor.
The factors of 86 are 1, 2, 43, 86
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The HCF of 86,360,108 is 2.
Lets's calculate GCF of 86,360,108
| 2 | 86, 360, 108 |
| 43, 180, 54 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 86,360,108 By Matching Biggest Common Factor Method
Now, list down the factors of 86
:1,2,43,86
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Greatest Common Factor
We found the factors 86,360,108 . The biggest common factor number is the GCF number.
So the greatest common factor 86,360,108 is 2.
Lets's calculate LCM of 77,52,208
| 2 | 77, 52, 208 |
| 2 | 77, 26, 104 |
| 13 | 77, 13, 52 |
| 77, 1, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 13 x 77 x 1 x 4 = 16016
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/16016
Therefore, the GCF of Fractions 86/77,360/52,108/208 is 2/16016
Least Common Multiple of 77,52,208 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 77,52,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,52,208) = 1
common factors(in case of two or more numbers have common factors) = 52
GCF(77,52,208) x common factors =1 x 52 = 52
LCM(77,52,208) = ( 77 × 52 × 208 ) / 52
LCM(77,52,208) = 832832 / 52
LCM(77,52,208) = 16016
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FAQs on GCF of Fractions of 86/77, 360/52, 108/208
1. What is the HCF of 86,360,108?
The HCF of 86,360,108 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 86/77, 360/52, 108/208?
Answer: GCF of Numerators as per given numbers 86/77, 360/52, 108/208 is
GCF of Numerators i.e. for 86,360,108 is 2
LCM of denominators i.e. for 77,52,208 is 16016.
Thus, GCF of Fractions is 2/16016.Finally, GCF of Fractions for 86/77, 360/52, 108/208 is 2/16016.