GCF of 872/660, 6978/210
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 872/660, 6978/210 i.e 2/4620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 872/660, 6978/210.
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 872/660,6978/210?
Given fractions are 872/660,6978/210
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 872/660,6978/210, numerators are 872,6978
Denominators are 660,210
The GCF of 872,6978 is 2 .
LCM of 660,210 is 4620.
The greatest common factor of 872/660,6978/210 = [GCF of 872,6978]/[LCM of 660,210]= 2/4620
Therefore, the GCF of 872/660,6978/210 is 2/4620.
To find the highest common factor of 872,6978, we have to find the factors of both numbers and list the highest common factor.
The factors of 872 are 1, 2, 4, 8, 109, 218, 436, 872
The factors of 6978 are 1, 2, 3, 6, 1163, 2326, 3489, 6978
The HCF of 872,6978 is 2.
Lets's calculate GCF of 872,6978
| 2 | 872, 6978 |
| 436, 3489 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 872,6978 By Matching Biggest Common Factor Method
Now, list down the factors of 872
:1,2,4,8,109,218,436,872
Now, list down the factors of 6978
:1,2,3,6,1163,2326,3489,6978
Greatest Common Factor
We found the factors 872,6978 . The biggest common factor number is the GCF number.
So the greatest common factor 872,6978 is 2.
Lets's calculate LCM of 660,210
| 2 | 660, 210 |
| 3 | 330, 105 |
| 5 | 110, 35 |
| 22, 7 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 22 x 7 = 4620
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4620
Therefore, the GCF of Fractions 872/660,6978/210 is 2/4620
Least Common Multiple of 660,210 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 660,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(660,210) = 30
common factors(in case of two or more numbers have common factors) = 1
GCF(660,210) x common factors =30 x 1 = 30
LCM(660,210) = ( 660 × 210 ) / 30
LCM(660,210) = 138600 / 30
LCM(660,210) = 4620
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FAQs on GCF of Fractions of 872/660, 6978/210
1. What is the HCF of 872,6978?
The HCF of 872,6978 is 2
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 872/660, 6978/210?
Answer: GCF of Numerators as per given numbers 872/660, 6978/210 is
GCF of Numerators i.e. for 872,6978 is 2
LCM of denominators i.e. for 660,210 is 4620.
Thus, GCF of Fractions is 2/4620.Finally, GCF of Fractions for 872/660, 6978/210 is 2/4620.