GCF of 706/21, 678/249
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 706/21, 678/249 i.e 2/1743 easily. The following is the detailed procedure to determine the greatest common factor of fractions 706/21, 678/249.
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 706/21,678/249?
Given fractions are 706/21,678/249
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 706/21,678/249, numerators are 706,678
Denominators are 21,249
The GCF of 706,678 is 2 .
LCM of 21,249 is 1743.
The greatest common factor of 706/21,678/249 = [GCF of 706,678]/[LCM of 21,249]= 2/1743
Therefore, the GCF of 706/21,678/249 is 2/1743.
To find the highest common factor of 706,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 706 are 1, 2, 353, 706
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 706,678 is 2.
Lets's calculate GCF of 706,678
| 2 | 706, 678 |
| 353, 339 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 706,678 By Matching Biggest Common Factor Method
Now, list down the factors of 706
:1,2,353,706
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 706,678 . The biggest common factor number is the GCF number.
So the greatest common factor 706,678 is 2.
Lets's calculate LCM of 21,249
| 3 | 21, 249 |
| 7, 83 |
∴ So the LCM of the given numbers is 3 x 7 x 83 = 1743
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1743
Therefore, the GCF of Fractions 706/21,678/249 is 2/1743
Least Common Multiple of 21,249 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 21,249 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,249) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(21,249) x common factors =3 x 1 = 3
LCM(21,249) = ( 21 × 249 ) / 3
LCM(21,249) = 5229 / 3
LCM(21,249) = 1743
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FAQs on GCF of Fractions of 706/21, 678/249
1. What is the HCF of 706,678?
The HCF of 706,678 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 706/21, 678/249?
Answer: GCF of Numerators as per given numbers 706/21, 678/249 is
GCF of Numerators i.e. for 706,678 is 2
LCM of denominators i.e. for 21,249 is 1743.
Thus, GCF of Fractions is 2/1743.Finally, GCF of Fractions for 706/21, 678/249 is 2/1743.