GCF of 2814/153, 8178/3540
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2814/153, 8178/3540 i.e 6/180540 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2814/153, 8178/3540.
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 2814/153,8178/3540?
Given fractions are 2814/153,8178/3540
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 2814/153,8178/3540, numerators are 2814,8178
Denominators are 153,3540
The GCF of 2814,8178 is 6 .
LCM of 153,3540 is 180540.
The greatest common factor of 2814/153,8178/3540 = [GCF of 2814,8178]/[LCM of 153,3540]= 6/180540
Therefore, the GCF of 2814/153,8178/3540 is 6/180540.
To find the highest common factor of 2814,8178, we have to find the factors of both numbers and list the highest common factor.
The factors of 2814 are 1, 2, 3, 6, 7, 14, 21, 42, 67, 134, 201, 402, 469, 938, 1407, 2814
The factors of 8178 are 1, 2, 3, 6, 29, 47, 58, 87, 94, 141, 174, 282, 1363, 2726, 4089, 8178
The HCF of 2814,8178 is 6.
Lets's calculate GCF of 2814,8178
| 2 | 2814, 8178 |
| 3 | 1407, 4089 |
| 469, 1363 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 2814,8178 By Matching Biggest Common Factor Method
Now, list down the factors of 2814
:1,2,3,6,7,14,21,42,67,134,201,402,469,938,1407,2814
Now, list down the factors of 8178
:1,2,3,6,29,47,58,87,94,141,174,282,1363,2726,4089,8178
Greatest Common Factor
We found the factors 2814,8178 . The biggest common factor number is the GCF number.
So the greatest common factor 2814,8178 is 6.
Lets's calculate LCM of 153,3540
| 3 | 153, 3540 |
| 51, 1180 |
∴ So the LCM of the given numbers is 3 x 51 x 1180 = 180540
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/180540
Therefore, the GCF of Fractions 2814/153,8178/3540 is 6/180540
Least Common Multiple of 153,3540 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 153,3540 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(153,3540) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(153,3540) x common factors =3 x 1 = 3
LCM(153,3540) = ( 153 × 3540 ) / 3
LCM(153,3540) = 541620 / 3
LCM(153,3540) = 180540
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 2814/153, 8178/3540
1. What is the HCF of 2814,8178?
The HCF of 2814,8178 is 6
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 2814/153, 8178/3540?
Answer: GCF of Numerators as per given numbers 2814/153, 8178/3540 is
GCF of Numerators i.e. for 2814,8178 is 6
LCM of denominators i.e. for 153,3540 is 180540.
Thus, GCF of Fractions is 6/180540.Finally, GCF of Fractions for 2814/153, 8178/3540 is 6/180540.