GCF of 967/309, 656/409
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 967/309, 656/409 i.e 1/126381 easily. The following is the detailed procedure to determine the greatest common factor of fractions 967/309, 656/409.
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 967/309,656/409?
Given fractions are 967/309,656/409
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 967/309,656/409, numerators are 967,656
Denominators are 309,409
The GCF of 967,656 is 1 .
LCM of 309,409 is 126381.
The greatest common factor of 967/309,656/409 = [GCF of 967,656]/[LCM of 309,409]= 1/126381
Therefore, the GCF of 967/309,656/409 is 1/126381.
To find the highest common factor of 967,656, we have to find the factors of both numbers and list the highest common factor.
The factors of 967 are 1, 967
The factors of 656 are 1, 2, 4, 8, 16, 41, 82, 164, 328, 656
The HCF of 967,656 is 1.
Lets's calculate GCF of 967,656
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 967,656 By Matching Biggest Common Factor Method
Now, list down the factors of 967
:1,967
Now, list down the factors of 656
:1,2,4,8,16,41,82,164,328,656
Greatest Common Factor
We found the factors 967,656 . The biggest common factor number is the GCF number.
So the greatest common factor 967,656 is 1.
Lets's calculate LCM of 309,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 126381
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/126381
Therefore, the GCF of Fractions 967/309,656/409 is 1/126381
Least Common Multiple of 309,409 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 309,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(309,409) x common factors =1 x 1 = 1
LCM(309,409) = ( 309 × 409 ) / 1
LCM(309,409) = 126381 / 1
LCM(309,409) = 126381
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FAQs on GCF of Fractions of 967/309, 656/409
1. What is the HCF of 967,656?
The HCF of 967,656 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 967/309, 656/409?
Answer: GCF of Numerators as per given numbers 967/309, 656/409 is
GCF of Numerators i.e. for 967,656 is 1
LCM of denominators i.e. for 309,409 is 126381.
Thus, GCF of Fractions is 1/126381.Finally, GCF of Fractions for 967/309, 656/409 is 1/126381.