GCF of 422/706, 212/719
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 422/706, 212/719 i.e 2/507614 easily. The following is the detailed procedure to determine the greatest common factor of fractions 422/706, 212/719.
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 422/706,212/719?
Given fractions are 422/706,212/719
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 422/706,212/719, numerators are 422,212
Denominators are 706,719
The GCF of 422,212 is 2 .
LCM of 706,719 is 507614.
The greatest common factor of 422/706,212/719 = [GCF of 422,212]/[LCM of 706,719]= 2/507614
Therefore, the GCF of 422/706,212/719 is 2/507614.
To find the highest common factor of 422,212, we have to find the factors of both numbers and list the highest common factor.
The factors of 422 are 1, 2, 211, 422
The factors of 212 are 1, 2, 4, 53, 106, 212
The HCF of 422,212 is 2.
Lets's calculate GCF of 422,212
| 2 | 422, 212 |
| 211, 106 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 422,212 By Matching Biggest Common Factor Method
Now, list down the factors of 422
:1,2,211,422
Now, list down the factors of 212
:1,2,4,53,106,212
Greatest Common Factor
We found the factors 422,212 . The biggest common factor number is the GCF number.
So the greatest common factor 422,212 is 2.
Lets's calculate LCM of 706,719
Given numbers has no common factors except 1. So, there LCM is their product i.e 507614
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/507614
Therefore, the GCF of Fractions 422/706,212/719 is 2/507614
Least Common Multiple of 706,719 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 706,719 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(706,719) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(706,719) x common factors =1 x 1 = 1
LCM(706,719) = ( 706 × 719 ) / 1
LCM(706,719) = 507614 / 1
LCM(706,719) = 507614
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FAQs on GCF of Fractions of 422/706, 212/719
1. What is the HCF of 422,212?
The HCF of 422,212 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 422/706, 212/719?
Answer: GCF of Numerators as per given numbers 422/706, 212/719 is
GCF of Numerators i.e. for 422,212 is 2
LCM of denominators i.e. for 706,719 is 507614.
Thus, GCF of Fractions is 2/507614.Finally, GCF of Fractions for 422/706, 212/719 is 2/507614.