GCF of 134/275, 1006/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 134/275, 1006/678 i.e 2/186450 easily. The following is the detailed procedure to determine the greatest common factor of fractions 134/275, 1006/678.
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 134/275,1006/678?
Given fractions are 134/275,1006/678
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 134/275,1006/678, numerators are 134,1006
Denominators are 275,678
The GCF of 134,1006 is 2 .
LCM of 275,678 is 186450.
The greatest common factor of 134/275,1006/678 = [GCF of 134,1006]/[LCM of 275,678]= 2/186450
Therefore, the GCF of 134/275,1006/678 is 2/186450.
To find the highest common factor of 134,1006, we have to find the factors of both numbers and list the highest common factor.
The factors of 134 are 1, 2, 67, 134
The factors of 1006 are 1, 2, 503, 1006
The HCF of 134,1006 is 2.
Lets's calculate GCF of 134,1006
| 2 | 134, 1006 |
| 67, 503 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 134,1006 By Matching Biggest Common Factor Method
Now, list down the factors of 134
:1,2,67,134
Now, list down the factors of 1006
:1,2,503,1006
Greatest Common Factor
We found the factors 134,1006 . The biggest common factor number is the GCF number.
So the greatest common factor 134,1006 is 2.
Lets's calculate LCM of 275,678
Given numbers has no common factors except 1. So, there LCM is their product i.e 186450
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/186450
Therefore, the GCF of Fractions 134/275,1006/678 is 2/186450
Least Common Multiple of 275,678 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 275,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(275,678) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(275,678) x common factors =1 x 1 = 1
LCM(275,678) = ( 275 × 678 ) / 1
LCM(275,678) = 186450 / 1
LCM(275,678) = 186450
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FAQs on GCF of Fractions of 134/275, 1006/678
1. What is the HCF of 134,1006?
The HCF of 134,1006 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 134/275, 1006/678?
Answer: GCF of Numerators as per given numbers 134/275, 1006/678 is
GCF of Numerators i.e. for 134,1006 is 2
LCM of denominators i.e. for 275,678 is 186450.
Thus, GCF of Fractions is 2/186450.Finally, GCF of Fractions for 134/275, 1006/678 is 2/186450.