GCF of 810/14, 140/278
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 810/14, 140/278 i.e 10/1946 easily. The following is the detailed procedure to determine the greatest common factor of fractions 810/14, 140/278.
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 810/14,140/278?
Given fractions are 810/14,140/278
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 810/14,140/278, numerators are 810,140
Denominators are 14,278
The GCF of 810,140 is 10 .
LCM of 14,278 is 1946.
The greatest common factor of 810/14,140/278 = [GCF of 810,140]/[LCM of 14,278]= 10/1946
Therefore, the GCF of 810/14,140/278 is 10/1946.
To find the highest common factor of 810,140, we have to find the factors of both numbers and list the highest common factor.
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The HCF of 810,140 is 10.
Lets's calculate GCF of 810,140
| 2 | 810, 140 |
| 5 | 405, 70 |
| 81, 14 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 810,140 By Matching Biggest Common Factor Method
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Now, list down the factors of 140
:1,2,4,5,7,10,14,20,28,35,70,140
Greatest Common Factor
We found the factors 810,140 . The biggest common factor number is the GCF number.
So the greatest common factor 810,140 is 10.
Lets's calculate LCM of 14,278
| 2 | 14, 278 |
| 7, 139 |
∴ So the LCM of the given numbers is 2 x 7 x 139 = 1946
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/1946
Therefore, the GCF of Fractions 810/14,140/278 is 10/1946
Least Common Multiple of 14,278 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 14,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,278) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(14,278) x common factors =2 x 1 = 2
LCM(14,278) = ( 14 × 278 ) / 2
LCM(14,278) = 3892 / 2
LCM(14,278) = 1946
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FAQs on GCF of Fractions of 810/14, 140/278
1. What is the HCF of 810,140?
The HCF of 810,140 is 10
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 810/14, 140/278?
Answer: GCF of Numerators as per given numbers 810/14, 140/278 is
GCF of Numerators i.e. for 810,140 is 10
LCM of denominators i.e. for 14,278 is 1946.
Thus, GCF of Fractions is 10/1946.Finally, GCF of Fractions for 810/14, 140/278 is 10/1946.