GCF of 422/991, 1914/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 422/991, 1914/214 i.e 2/212074 easily. The following is the detailed procedure to determine the greatest common factor of fractions 422/991, 1914/214.
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 422/991,1914/214?
Given fractions are 422/991,1914/214
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 422/991,1914/214, numerators are 422,1914
Denominators are 991,214
The GCF of 422,1914 is 2 .
LCM of 991,214 is 212074.
The greatest common factor of 422/991,1914/214 = [GCF of 422,1914]/[LCM of 991,214]= 2/212074
Therefore, the GCF of 422/991,1914/214 is 2/212074.
To find the highest common factor of 422,1914, 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 1914 are 1, 2, 3, 6, 11, 22, 29, 33, 58, 66, 87, 174, 319, 638, 957, 1914
The HCF of 422,1914 is 2.
Lets's calculate GCF of 422,1914
| 2 | 422, 1914 |
| 211, 957 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 422,1914 By Matching Biggest Common Factor Method
Now, list down the factors of 422
:1,2,211,422
Now, list down the factors of 1914
:1,2,3,6,11,22,29,33,58,66,87,174,319,638,957,1914
Greatest Common Factor
We found the factors 422,1914 . The biggest common factor number is the GCF number.
So the greatest common factor 422,1914 is 2.
Lets's calculate LCM of 991,214
Given numbers has no common factors except 1. So, there LCM is their product i.e 212074
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/212074
Therefore, the GCF of Fractions 422/991,1914/214 is 2/212074
Least Common Multiple of 991,214 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 991,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(991,214) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(991,214) x common factors =1 x 1 = 1
LCM(991,214) = ( 991 × 214 ) / 1
LCM(991,214) = 212074 / 1
LCM(991,214) = 212074
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FAQs on GCF of Fractions of 422/991, 1914/214
1. What is the HCF of 422,1914?
The HCF of 422,1914 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 422/991, 1914/214?
Answer: GCF of Numerators as per given numbers 422/991, 1914/214 is
GCF of Numerators i.e. for 422,1914 is 2
LCM of denominators i.e. for 991,214 is 212074.
Thus, GCF of Fractions is 2/212074.Finally, GCF of Fractions for 422/991, 1914/214 is 2/212074.