GCF of 7917/218, 2970/168
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7917/218, 2970/168 i.e 3/18312 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7917/218, 2970/168.
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 7917/218,2970/168?
Given fractions are 7917/218,2970/168
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 7917/218,2970/168, numerators are 7917,2970
Denominators are 218,168
The GCF of 7917,2970 is 3 .
LCM of 218,168 is 18312.
The greatest common factor of 7917/218,2970/168 = [GCF of 7917,2970]/[LCM of 218,168]= 3/18312
Therefore, the GCF of 7917/218,2970/168 is 3/18312.
To find the highest common factor of 7917,2970, we have to find the factors of both numbers and list the highest common factor.
The factors of 7917 are 1, 3, 7, 13, 21, 29, 39, 87, 91, 203, 273, 377, 609, 1131, 2639, 7917
The factors of 2970 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 27, 30, 33, 45, 54, 55, 66, 90, 99, 110, 135, 165, 198, 270, 297, 330, 495, 594, 990, 1485, 2970
The HCF of 7917,2970 is 3.
Lets's calculate GCF of 7917,2970
| 3 | 7917, 2970 |
| 2639, 990 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7917,2970 By Matching Biggest Common Factor Method
Now, list down the factors of 7917
:1,3,7,13,21,29,39,87,91,203,273,377,609,1131,2639,7917
Now, list down the factors of 2970
:1,2,3,5,6,9,10,11,15,18,22,27,30,33,45,54,55,66,90,99,110,135,165,198,270,297,330,495,594,990,1485,2970
Greatest Common Factor
We found the factors 7917,2970 . The biggest common factor number is the GCF number.
So the greatest common factor 7917,2970 is 3.
Lets's calculate LCM of 218,168
| 2 | 218, 168 |
| 109, 84 |
∴ So the LCM of the given numbers is 2 x 109 x 84 = 18312
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/18312
Therefore, the GCF of Fractions 7917/218,2970/168 is 3/18312
Least Common Multiple of 218,168 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 218,168 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(218,168) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(218,168) x common factors =2 x 1 = 2
LCM(218,168) = ( 218 × 168 ) / 2
LCM(218,168) = 36624 / 2
LCM(218,168) = 18312
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FAQs on GCF of Fractions of 7917/218, 2970/168
1. What is the HCF of 7917,2970?
The HCF of 7917,2970 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 7917/218, 2970/168?
Answer: GCF of Numerators as per given numbers 7917/218, 2970/168 is
GCF of Numerators i.e. for 7917,2970 is 3
LCM of denominators i.e. for 218,168 is 18312.
Thus, GCF of Fractions is 3/18312.Finally, GCF of Fractions for 7917/218, 2970/168 is 3/18312.