GCF of 812/40, 317/70, 219/70
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 812/40, 317/70, 219/70 i.e 1/280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/40, 317/70, 219/70.
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 812/40,317/70,219/70?
Given fractions are 812/40,317/70,219/70
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 812/40,317/70,219/70, numerators are 812,317,219
Denominators are 40,70,70
The GCF of 812,317,219 is 1 .
LCM of 40,70,70 is 280.
The greatest common factor of 812/40,317/70,219/70 = [GCF of 812,317,219]/[LCM of 40,70,70]= 1/280
Therefore, the GCF of 812/40,317/70,219/70 is 1/280.
To find the highest common factor of 812,317,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
The factors of 317 are 1, 317
The factors of 219 are 1, 3, 73, 219
The HCF of 812,317,219 is 1.
Lets's calculate GCF of 812,317,219
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 812,317,219 By Matching Biggest Common Factor Method
Now, list down the factors of 812
:1,2,4,7,14,28,29,58,116,203,406,812
Now, list down the factors of 317
:1,317
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 812,317,219 . The biggest common factor number is the GCF number.
So the greatest common factor 812,317,219 is 1.
Lets's calculate LCM of 40,70,70
| 2 | 40, 70, 70 |
| 5 | 20, 35, 35 |
| 7 | 4, 7, 7 |
| 4, 1, 1 |
∴ So the LCM of the given numbers is 2 x 5 x 7 x 4 x 1 x 1 = 280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/280
Therefore, the GCF of Fractions 812/40,317/70,219/70 is 1/280
Least Common Multiple of 40,70,70 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 40,70,70 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,70,70) = 10
common factors(in case of two or more numbers have common factors) = 70
GCF(40,70,70) x common factors =10 x 70 = 700
LCM(40,70,70) = ( 40 × 70 × 70 ) / 700
LCM(40,70,70) = 196000 / 700
LCM(40,70,70) = 280
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FAQs on GCF of Fractions of 812/40, 317/70, 219/70
1. What is the HCF of 812,317,219?
The HCF of 812,317,219 is 1
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 812/40, 317/70, 219/70?
Answer: GCF of Numerators as per given numbers 812/40, 317/70, 219/70 is
GCF of Numerators i.e. for 812,317,219 is 1
LCM of denominators i.e. for 40,70,70 is 280.
Thus, GCF of Fractions is 1/280.Finally, GCF of Fractions for 812/40, 317/70, 219/70 is 1/280.