GCF of 876/780, 657/820
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 876/780, 657/820 i.e 219/31980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 876/780, 657/820.
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 876/780,657/820?
Given fractions are 876/780,657/820
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 876/780,657/820, numerators are 876,657
Denominators are 780,820
The GCF of 876,657 is 219 .
LCM of 780,820 is 31980.
The greatest common factor of 876/780,657/820 = [GCF of 876,657]/[LCM of 780,820]= 219/31980
Therefore, the GCF of 876/780,657/820 is 219/31980.
To find the highest common factor of 876,657, we have to find the factors of both numbers and list the highest common factor.
The factors of 876 are 1, 2, 3, 4, 6, 12, 73, 146, 219, 292, 438, 876
The factors of 657 are 1, 3, 9, 73, 219, 657
The HCF of 876,657 is 219.
Lets's calculate GCF of 876,657
| 3 | 876, 657 |
| 73 | 292, 219 |
| 4, 3 |
∴ So the GCF of the given numbers is 3 x 73 = 219
Greatest Common Factor of 876,657 By Matching Biggest Common Factor Method
Now, list down the factors of 876
:1,2,3,4,6,12,73,146,219,292,438,876
Now, list down the factors of 657
:1,3,9,73,219,657
Greatest Common Factor
We found the factors 876,657 . The biggest common factor number is the GCF number.
So the greatest common factor 876,657 is 219.
Lets's calculate LCM of 780,820
| 2 | 780, 820 |
| 2 | 390, 410 |
| 5 | 195, 205 |
| 39, 41 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 39 x 41 = 31980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 219/31980
Therefore, the GCF of Fractions 876/780,657/820 is 219/31980
Least Common Multiple of 780,820 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 780,820 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(780,820) = 20
common factors(in case of two or more numbers have common factors) = 1
GCF(780,820) x common factors =20 x 1 = 20
LCM(780,820) = ( 780 × 820 ) / 20
LCM(780,820) = 639600 / 20
LCM(780,820) = 31980
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 876/780, 657/820
1. What is the HCF of 876,657?
The HCF of 876,657 is 219
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 876/780, 657/820?
Answer: GCF of Numerators as per given numbers 876/780, 657/820 is
GCF of Numerators i.e. for 876,657 is 219
LCM of denominators i.e. for 780,820 is 31980.
Thus, GCF of Fractions is 219/31980.Finally, GCF of Fractions for 876/780, 657/820 is 219/31980.