GCF of 726/64, 506/217
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 726/64, 506/217 i.e 22/13888 easily. The following is the detailed procedure to determine the greatest common factor of fractions 726/64, 506/217.
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 726/64,506/217?
Given fractions are 726/64,506/217
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 726/64,506/217, numerators are 726,506
Denominators are 64,217
The GCF of 726,506 is 22 .
LCM of 64,217 is 13888.
The greatest common factor of 726/64,506/217 = [GCF of 726,506]/[LCM of 64,217]= 22/13888
Therefore, the GCF of 726/64,506/217 is 22/13888.
To find the highest common factor of 726,506, we have to find the factors of both numbers and list the highest common factor.
The factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726
The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506
The HCF of 726,506 is 22.
Lets's calculate GCF of 726,506
| 2 | 726, 506 |
| 11 | 363, 253 |
| 33, 23 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 726,506 By Matching Biggest Common Factor Method
Now, list down the factors of 726
:1,2,3,6,11,22,33,66,121,242,363,726
Now, list down the factors of 506
:1,2,11,22,23,46,253,506
Greatest Common Factor
We found the factors 726,506 . The biggest common factor number is the GCF number.
So the greatest common factor 726,506 is 22.
Lets's calculate LCM of 64,217
Given numbers has no common factors except 1. So, there LCM is their product i.e 13888
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/13888
Therefore, the GCF of Fractions 726/64,506/217 is 22/13888
Least Common Multiple of 64,217 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 64,217 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,217) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(64,217) x common factors =1 x 1 = 1
LCM(64,217) = ( 64 × 217 ) / 1
LCM(64,217) = 13888 / 1
LCM(64,217) = 13888
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FAQs on GCF of Fractions of 726/64, 506/217
1. What is the HCF of 726,506?
The HCF of 726,506 is 22
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 726/64, 506/217?
Answer: GCF of Numerators as per given numbers 726/64, 506/217 is
GCF of Numerators i.e. for 726,506 is 22
LCM of denominators i.e. for 64,217 is 13888.
Thus, GCF of Fractions is 22/13888.Finally, GCF of Fractions for 726/64, 506/217 is 22/13888.