GCF of 68/132, 24/269, 210/287
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 68/132, 24/269, 210/287 i.e 2/10190796 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/132, 24/269, 210/287.
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 68/132,24/269,210/287?
Given fractions are 68/132,24/269,210/287
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 68/132,24/269,210/287, numerators are 68,24,210
Denominators are 132,269,287
The GCF of 68,24,210 is 2 .
LCM of 132,269,287 is 10190796.
The greatest common factor of 68/132,24/269,210/287 = [GCF of 68,24,210]/[LCM of 132,269,287]= 2/10190796
Therefore, the GCF of 68/132,24/269,210/287 is 2/10190796.
To find the highest common factor of 68,24,210, we have to find the factors of both numbers and list the highest common factor.
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 68,24,210 is 2.
Lets's calculate GCF of 68,24,210
| 2 | 68, 24, 210 |
| 34, 12, 105 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 68,24,210 By Matching Biggest Common Factor Method
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 24
:1,2,3,4,6,8,12,24
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 68,24,210 . The biggest common factor number is the GCF number.
So the greatest common factor 68,24,210 is 2.
Lets's calculate LCM of 132,269,287
Given numbers has no common factors except 1. So, there LCM is their product i.e 10190796
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/10190796
Therefore, the GCF of Fractions 68/132,24/269,210/287 is 2/10190796
Least Common Multiple of 132,269,287 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 132,269,287 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(132,269,287) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(132,269,287) x common factors =1 x 1 = 1
LCM(132,269,287) = ( 132 × 269 × 287 ) / 1
LCM(132,269,287) = 10190796 / 1
LCM(132,269,287) = 10190796
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FAQs on GCF of Fractions of 68/132, 24/269, 210/287
1. What is the HCF of 68,24,210?
The HCF of 68,24,210 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 68/132, 24/269, 210/287?
Answer: GCF of Numerators as per given numbers 68/132, 24/269, 210/287 is
GCF of Numerators i.e. for 68,24,210 is 2
LCM of denominators i.e. for 132,269,287 is 10190796.
Thus, GCF of Fractions is 2/10190796.Finally, GCF of Fractions for 68/132, 24/269, 210/287 is 2/10190796.