GCF of 852/214, 413/530
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 852/214, 413/530 i.e 1/56710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 852/214, 413/530.
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 852/214,413/530?
Given fractions are 852/214,413/530
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 852/214,413/530, numerators are 852,413
Denominators are 214,530
The GCF of 852,413 is 1 .
LCM of 214,530 is 56710.
The greatest common factor of 852/214,413/530 = [GCF of 852,413]/[LCM of 214,530]= 1/56710
Therefore, the GCF of 852/214,413/530 is 1/56710.
To find the highest common factor of 852,413, we have to find the factors of both numbers and list the highest common factor.
The factors of 852 are 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852
The factors of 413 are 1, 7, 59, 413
The HCF of 852,413 is 1.
Lets's calculate GCF of 852,413
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 852,413 By Matching Biggest Common Factor Method
Now, list down the factors of 852
:1,2,3,4,6,12,71,142,213,284,426,852
Now, list down the factors of 413
:1,7,59,413
Greatest Common Factor
We found the factors 852,413 . The biggest common factor number is the GCF number.
So the greatest common factor 852,413 is 1.
Lets's calculate LCM of 214,530
| 2 | 214, 530 |
| 107, 265 |
∴ So the LCM of the given numbers is 2 x 107 x 265 = 56710
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/56710
Therefore, the GCF of Fractions 852/214,413/530 is 1/56710
Least Common Multiple of 214,530 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 214,530 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,530) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(214,530) x common factors =2 x 1 = 2
LCM(214,530) = ( 214 × 530 ) / 2
LCM(214,530) = 113420 / 2
LCM(214,530) = 56710
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FAQs on GCF of Fractions of 852/214, 413/530
1. What is the HCF of 852,413?
The HCF of 852,413 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 852/214, 413/530?
Answer: GCF of Numerators as per given numbers 852/214, 413/530 is
GCF of Numerators i.e. for 852,413 is 1
LCM of denominators i.e. for 214,530 is 56710.
Thus, GCF of Fractions is 1/56710.Finally, GCF of Fractions for 852/214, 413/530 is 1/56710.