Use our free GCF of Fractions Calculator tool to compute the GCF of 841/825, 780/209 i.e 1/15675 easily. The following is the detailed procedure to determine the greatest common factor of fractions 841/825, 780/209.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 841/825,780/209
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 841/825,780/209, numerators are 841,780
Denominators are 825,209
The GCF of 841,780 is 1 .
LCM of 825,209 is 15675.
The greatest common factor of 841/825,780/209 = [GCF of 841,780]/[LCM of 825,209]= 1/15675
Therefore, the GCF of 841/825,780/209 is 1/15675.
To find the highest common factor of 841,780, we have to find the factors of both numbers and list the highest common factor.
The factors of 841 are 1, 29, 841
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The HCF of 841,780 is 1.
Lets's calculate GCF of 841,780
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 841
:1,29,841
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Greatest Common Factor
We found the factors 841,780 . The biggest common factor number is the GCF number.
So the greatest common factor 841,780 is 1.
Lets's calculate LCM of 825,209
11 | 825, 209 |
75, 19 |
∴ So the LCM of the given numbers is 11 x 75 x 19 = 15675
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15675
Therefore, the GCF of Fractions 841/825,780/209 is 1/15675
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 825,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(825,209) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(825,209) x common factors =11 x 1 = 11
LCM(825,209) = ( 825 × 209 ) / 11
LCM(825,209) = 172425 / 11
LCM(825,209) = 15675
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 841,780?
The HCF of 841,780 is 1
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 841/825, 780/209?
Answer: GCF of Numerators as per given numbers 841/825, 780/209 is
GCF of Numerators i.e. for 841,780 is 1
LCM of denominators i.e. for 825,209 is 15675.
Thus, GCF of Fractions is 1/15675.Finally, GCF of Fractions for 841/825, 780/209 is 1/15675.