GCF of 867/390, 420/258
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 867/390, 420/258 i.e 3/16770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 867/390, 420/258.
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 867/390,420/258?
Given fractions are 867/390,420/258
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 867/390,420/258, numerators are 867,420
Denominators are 390,258
The GCF of 867,420 is 3 .
LCM of 390,258 is 16770.
The greatest common factor of 867/390,420/258 = [GCF of 867,420]/[LCM of 390,258]= 3/16770
Therefore, the GCF of 867/390,420/258 is 3/16770.
To find the highest common factor of 867,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 867 are 1, 3, 17, 51, 289, 867
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 867,420 is 3.
Lets's calculate GCF of 867,420
| 3 | 867, 420 |
| 289, 140 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 867,420 By Matching Biggest Common Factor Method
Now, list down the factors of 867
:1,3,17,51,289,867
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 867,420 . The biggest common factor number is the GCF number.
So the greatest common factor 867,420 is 3.
Lets's calculate LCM of 390,258
| 2 | 390, 258 |
| 3 | 195, 129 |
| 65, 43 |
∴ So the LCM of the given numbers is 2 x 3 x 65 x 43 = 16770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/16770
Therefore, the GCF of Fractions 867/390,420/258 is 3/16770
Least Common Multiple of 390,258 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 390,258 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(390,258) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(390,258) x common factors =6 x 1 = 6
LCM(390,258) = ( 390 × 258 ) / 6
LCM(390,258) = 100620 / 6
LCM(390,258) = 16770
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 867/390, 420/258
1. What is the HCF of 867,420?
The HCF of 867,420 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 867/390, 420/258?
Answer: GCF of Numerators as per given numbers 867/390, 420/258 is
GCF of Numerators i.e. for 867,420 is 3
LCM of denominators i.e. for 390,258 is 16770.
Thus, GCF of Fractions is 3/16770.Finally, GCF of Fractions for 867/390, 420/258 is 3/16770.