GCF of 729/67, 214/6920
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 729/67, 214/6920 i.e 1/463640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 729/67, 214/6920.
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 729/67,214/6920?
Given fractions are 729/67,214/6920
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 729/67,214/6920, numerators are 729,214
Denominators are 67,6920
The GCF of 729,214 is 1 .
LCM of 67,6920 is 463640.
The greatest common factor of 729/67,214/6920 = [GCF of 729,214]/[LCM of 67,6920]= 1/463640
Therefore, the GCF of 729/67,214/6920 is 1/463640.
To find the highest common factor of 729,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 729 are 1, 3, 9, 27, 81, 243, 729
The factors of 214 are 1, 2, 107, 214
The HCF of 729,214 is 1.
Lets's calculate GCF of 729,214
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 729,214 By Matching Biggest Common Factor Method
Now, list down the factors of 729
:1,3,9,27,81,243,729
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 729,214 . The biggest common factor number is the GCF number.
So the greatest common factor 729,214 is 1.
Lets's calculate LCM of 67,6920
Given numbers has no common factors except 1. So, there LCM is their product i.e 463640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/463640
Therefore, the GCF of Fractions 729/67,214/6920 is 1/463640
Least Common Multiple of 67,6920 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 67,6920 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,6920) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(67,6920) x common factors =1 x 1 = 1
LCM(67,6920) = ( 67 × 6920 ) / 1
LCM(67,6920) = 463640 / 1
LCM(67,6920) = 463640
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FAQs on GCF of Fractions of 729/67, 214/6920
1. What is the HCF of 729,214?
The HCF of 729,214 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 729/67, 214/6920?
Answer: GCF of Numerators as per given numbers 729/67, 214/6920 is
GCF of Numerators i.e. for 729,214 is 1
LCM of denominators i.e. for 67,6920 is 463640.
Thus, GCF of Fractions is 1/463640.Finally, GCF of Fractions for 729/67, 214/6920 is 1/463640.