GCF of 763/54, 872/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 763/54, 872/209 i.e 109/11286 easily. The following is the detailed procedure to determine the greatest common factor of fractions 763/54, 872/209.
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 763/54,872/209?
Given fractions are 763/54,872/209
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 763/54,872/209, numerators are 763,872
Denominators are 54,209
The GCF of 763,872 is 109 .
LCM of 54,209 is 11286.
The greatest common factor of 763/54,872/209 = [GCF of 763,872]/[LCM of 54,209]= 109/11286
Therefore, the GCF of 763/54,872/209 is 109/11286.
To find the highest common factor of 763,872, we have to find the factors of both numbers and list the highest common factor.
The factors of 763 are 1, 7, 109, 763
The factors of 872 are 1, 2, 4, 8, 109, 218, 436, 872
The HCF of 763,872 is 109.
Lets's calculate GCF of 763,872
| 109 | 763, 872 |
| 7, 8 |
∴ So the GCF of the given numbers is 109 = 109
Greatest Common Factor of 763,872 By Matching Biggest Common Factor Method
Now, list down the factors of 763
:1,7,109,763
Now, list down the factors of 872
:1,2,4,8,109,218,436,872
Greatest Common Factor
We found the factors 763,872 . The biggest common factor number is the GCF number.
So the greatest common factor 763,872 is 109.
Lets's calculate LCM of 54,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 11286
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 109/11286
Therefore, the GCF of Fractions 763/54,872/209 is 109/11286
Least Common Multiple of 54,209 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 54,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(54,209) x common factors =1 x 1 = 1
LCM(54,209) = ( 54 × 209 ) / 1
LCM(54,209) = 11286 / 1
LCM(54,209) = 11286
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 763/54, 872/209
1. What is the HCF of 763,872?
The HCF of 763,872 is 109
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 763/54, 872/209?
Answer: GCF of Numerators as per given numbers 763/54, 872/209 is
GCF of Numerators i.e. for 763,872 is 109
LCM of denominators i.e. for 54,209 is 11286.
Thus, GCF of Fractions is 109/11286.Finally, GCF of Fractions for 763/54, 872/209 is 109/11286.