GCF of 105/807, 828/269
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 105/807, 828/269 i.e 3/807 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/807, 828/269.
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 105/807,828/269?
Given fractions are 105/807,828/269
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 105/807,828/269, numerators are 105,828
Denominators are 807,269
The GCF of 105,828 is 3 .
LCM of 807,269 is 807.
The greatest common factor of 105/807,828/269 = [GCF of 105,828]/[LCM of 807,269]= 3/807
Therefore, the GCF of 105/807,828/269 is 3/807.
To find the highest common factor of 105,828, we have to find the factors of both numbers and list the highest common factor.
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The HCF of 105,828 is 3.
Lets's calculate GCF of 105,828
| 3 | 105, 828 |
| 35, 276 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 105,828 By Matching Biggest Common Factor Method
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Now, list down the factors of 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Greatest Common Factor
We found the factors 105,828 . The biggest common factor number is the GCF number.
So the greatest common factor 105,828 is 3.
Lets's calculate LCM of 807,269
| 269 | 807, 269 |
| 3, 1 |
∴ So the LCM of the given numbers is 269 x 3 x 1 = 807
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/807
Therefore, the GCF of Fractions 105/807,828/269 is 3/807
Least Common Multiple of 807,269 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 807,269 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(807,269) = 269
common factors(in case of two or more numbers have common factors) = 1
GCF(807,269) x common factors =269 x 1 = 269
LCM(807,269) = ( 807 × 269 ) / 269
LCM(807,269) = 217083 / 269
LCM(807,269) = 807
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FAQs on GCF of Fractions of 105/807, 828/269
1. What is the HCF of 105,828?
The HCF of 105,828 is 3
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 105/807, 828/269?
Answer: GCF of Numerators as per given numbers 105/807, 828/269 is
GCF of Numerators i.e. for 105,828 is 3
LCM of denominators i.e. for 807,269 is 807.
Thus, GCF of Fractions is 3/807.Finally, GCF of Fractions for 105/807, 828/269 is 3/807.