GCF of 1869/821, 1278/2789
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1869/821, 1278/2789 i.e 3/2289769 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1869/821, 1278/2789.
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 1869/821,1278/2789?
Given fractions are 1869/821,1278/2789
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 1869/821,1278/2789, numerators are 1869,1278
Denominators are 821,2789
The GCF of 1869,1278 is 3 .
LCM of 821,2789 is 2289769.
The greatest common factor of 1869/821,1278/2789 = [GCF of 1869,1278]/[LCM of 821,2789]= 3/2289769
Therefore, the GCF of 1869/821,1278/2789 is 3/2289769.
To find the highest common factor of 1869,1278, we have to find the factors of both numbers and list the highest common factor.
The factors of 1869 are 1, 3, 7, 21, 89, 267, 623, 1869
The factors of 1278 are 1, 2, 3, 6, 9, 18, 71, 142, 213, 426, 639, 1278
The HCF of 1869,1278 is 3.
Lets's calculate GCF of 1869,1278
| 3 | 1869, 1278 |
| 623, 426 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1869,1278 By Matching Biggest Common Factor Method
Now, list down the factors of 1869
:1,3,7,21,89,267,623,1869
Now, list down the factors of 1278
:1,2,3,6,9,18,71,142,213,426,639,1278
Greatest Common Factor
We found the factors 1869,1278 . The biggest common factor number is the GCF number.
So the greatest common factor 1869,1278 is 3.
Lets's calculate LCM of 821,2789
Given numbers has no common factors except 1. So, there LCM is their product i.e 2289769
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2289769
Therefore, the GCF of Fractions 1869/821,1278/2789 is 3/2289769
Least Common Multiple of 821,2789 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 821,2789 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(821,2789) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(821,2789) x common factors =1 x 1 = 1
LCM(821,2789) = ( 821 × 2789 ) / 1
LCM(821,2789) = 2289769 / 1
LCM(821,2789) = 2289769
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FAQs on GCF of Fractions of 1869/821, 1278/2789
1. What is the HCF of 1869,1278?
The HCF of 1869,1278 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 1869/821, 1278/2789?
Answer: GCF of Numerators as per given numbers 1869/821, 1278/2789 is
GCF of Numerators i.e. for 1869,1278 is 3
LCM of denominators i.e. for 821,2789 is 2289769.
Thus, GCF of Fractions is 3/2289769.Finally, GCF of Fractions for 1869/821, 1278/2789 is 3/2289769.