GCF of 8/21, 398/89, 140/60
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8/21, 398/89, 140/60 i.e 2/37380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/21, 398/89, 140/60.
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 8/21,398/89,140/60?
Given fractions are 8/21,398/89,140/60
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 8/21,398/89,140/60, numerators are 8,398,140
Denominators are 21,89,60
The GCF of 8,398,140 is 2 .
LCM of 21,89,60 is 37380.
The greatest common factor of 8/21,398/89,140/60 = [GCF of 8,398,140]/[LCM of 21,89,60]= 2/37380
Therefore, the GCF of 8/21,398/89,140/60 is 2/37380.
To find the highest common factor of 8,398,140, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 398 are 1, 2, 199, 398
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The HCF of 8,398,140 is 2.
Lets's calculate GCF of 8,398,140
| 2 | 8, 398, 140 |
| 4, 199, 70 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8,398,140 By Matching Biggest Common Factor Method
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 398
:1,2,199,398
Now, list down the factors of 140
:1,2,4,5,7,10,14,20,28,35,70,140
Greatest Common Factor
We found the factors 8,398,140 . The biggest common factor number is the GCF number.
So the greatest common factor 8,398,140 is 2.
Lets's calculate LCM of 21,89,60
| 3 | 21, 89, 60 |
| 7, 89, 20 |
∴ So the LCM of the given numbers is 3 x 7 x 89 x 20 = 37380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/37380
Therefore, the GCF of Fractions 8/21,398/89,140/60 is 2/37380
Least Common Multiple of 21,89,60 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 21,89,60 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,89,60) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(21,89,60) x common factors =1 x 3 = 3
LCM(21,89,60) = ( 21 × 89 × 60 ) / 3
LCM(21,89,60) = 112140 / 3
LCM(21,89,60) = 37380
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FAQs on GCF of Fractions of 8/21, 398/89, 140/60
1. What is the HCF of 8,398,140?
The HCF of 8,398,140 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 8/21, 398/89, 140/60?
Answer: GCF of Numerators as per given numbers 8/21, 398/89, 140/60 is
GCF of Numerators i.e. for 8,398,140 is 2
LCM of denominators i.e. for 21,89,60 is 37380.
Thus, GCF of Fractions is 2/37380.Finally, GCF of Fractions for 8/21, 398/89, 140/60 is 2/37380.