GCF of 410/354, 969/394
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 410/354, 969/394 i.e 1/69738 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/354, 969/394.
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 410/354,969/394?
Given fractions are 410/354,969/394
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 410/354,969/394, numerators are 410,969
Denominators are 354,394
The GCF of 410,969 is 1 .
LCM of 354,394 is 69738.
The greatest common factor of 410/354,969/394 = [GCF of 410,969]/[LCM of 354,394]= 1/69738
Therefore, the GCF of 410/354,969/394 is 1/69738.
To find the highest common factor of 410,969, we have to find the factors of both numbers and list the highest common factor.
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969
The HCF of 410,969 is 1.
Lets's calculate GCF of 410,969
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 410,969 By Matching Biggest Common Factor Method
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Now, list down the factors of 969
:1,3,17,19,51,57,323,969
Greatest Common Factor
We found the factors 410,969 . The biggest common factor number is the GCF number.
So the greatest common factor 410,969 is 1.
Lets's calculate LCM of 354,394
| 2 | 354, 394 |
| 177, 197 |
∴ So the LCM of the given numbers is 2 x 177 x 197 = 69738
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/69738
Therefore, the GCF of Fractions 410/354,969/394 is 1/69738
Least Common Multiple of 354,394 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 354,394 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(354,394) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(354,394) x common factors =2 x 1 = 2
LCM(354,394) = ( 354 × 394 ) / 2
LCM(354,394) = 139476 / 2
LCM(354,394) = 69738
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FAQs on GCF of Fractions of 410/354, 969/394
1. What is the HCF of 410,969?
The HCF of 410,969 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 410/354, 969/394?
Answer: GCF of Numerators as per given numbers 410/354, 969/394 is
GCF of Numerators i.e. for 410,969 is 1
LCM of denominators i.e. for 354,394 is 69738.
Thus, GCF of Fractions is 1/69738.Finally, GCF of Fractions for 410/354, 969/394 is 1/69738.