GCF of 268/286, 975/156, 561/684
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 268/286, 975/156, 561/684 i.e 1/97812 easily. The following is the detailed procedure to determine the greatest common factor of fractions 268/286, 975/156, 561/684.
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 268/286,975/156,561/684?
Given fractions are 268/286,975/156,561/684
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 268/286,975/156,561/684, numerators are 268,975,561
Denominators are 286,156,684
The GCF of 268,975,561 is 1 .
LCM of 286,156,684 is 97812.
The greatest common factor of 268/286,975/156,561/684 = [GCF of 268,975,561]/[LCM of 286,156,684]= 1/97812
Therefore, the GCF of 268/286,975/156,561/684 is 1/97812.
To find the highest common factor of 268,975,561, we have to find the factors of both numbers and list the highest common factor.
The factors of 268 are 1, 2, 4, 67, 134, 268
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The factors of 561 are 1, 3, 11, 17, 33, 51, 187, 561
The HCF of 268,975,561 is 1.
Lets's calculate GCF of 268,975,561
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 268,975,561 By Matching Biggest Common Factor Method
Now, list down the factors of 268
:1,2,4,67,134,268
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Now, list down the factors of 561
:1,3,11,17,33,51,187,561
Greatest Common Factor
We found the factors 268,975,561 . The biggest common factor number is the GCF number.
So the greatest common factor 268,975,561 is 1.
Lets's calculate LCM of 286,156,684
| 2 | 286, 156, 684 |
| 2 | 143, 78, 342 |
| 3 | 143, 39, 171 |
| 13 | 143, 13, 57 |
| 11, 1, 57 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 11 x 1 x 57 = 97812
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/97812
Therefore, the GCF of Fractions 268/286,975/156,561/684 is 1/97812
Least Common Multiple of 286,156,684 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 286,156,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(286,156,684) = 2
common factors(in case of two or more numbers have common factors) = 156
GCF(286,156,684) x common factors =2 x 156 = 312
LCM(286,156,684) = ( 286 × 156 × 684 ) / 312
LCM(286,156,684) = 30517344 / 312
LCM(286,156,684) = 97812
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FAQs on GCF of Fractions of 268/286, 975/156, 561/684
1. What is the HCF of 268,975,561?
The HCF of 268,975,561 is 1
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 268/286, 975/156, 561/684?
Answer: GCF of Numerators as per given numbers 268/286, 975/156, 561/684 is
GCF of Numerators i.e. for 268,975,561 is 1
LCM of denominators i.e. for 286,156,684 is 97812.
Thus, GCF of Fractions is 1/97812.Finally, GCF of Fractions for 268/286, 975/156, 561/684 is 1/97812.