GCF of 86/268, 84/709, 315/449
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 86/268, 84/709, 315/449 i.e 1/85315388 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/268, 84/709, 315/449.
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 86/268,84/709,315/449?
Given fractions are 86/268,84/709,315/449
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 86/268,84/709,315/449, numerators are 86,84,315
Denominators are 268,709,449
The GCF of 86,84,315 is 1 .
LCM of 268,709,449 is 85315388.
The greatest common factor of 86/268,84/709,315/449 = [GCF of 86,84,315]/[LCM of 268,709,449]= 1/85315388
Therefore, the GCF of 86/268,84/709,315/449 is 1/85315388.
To find the highest common factor of 86,84,315, we have to find the factors of both numbers and list the highest common factor.
The factors of 86 are 1, 2, 43, 86
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
The HCF of 86,84,315 is 1.
Lets's calculate GCF of 86,84,315
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 86,84,315 By Matching Biggest Common Factor Method
Now, list down the factors of 86
:1,2,43,86
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 315
:1,3,5,7,9,15,21,35,45,63,105,315
Greatest Common Factor
We found the factors 86,84,315 . The biggest common factor number is the GCF number.
So the greatest common factor 86,84,315 is 1.
Lets's calculate LCM of 268,709,449
Given numbers has no common factors except 1. So, there LCM is their product i.e 85315388
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/85315388
Therefore, the GCF of Fractions 86/268,84/709,315/449 is 1/85315388
Least Common Multiple of 268,709,449 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 268,709,449 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(268,709,449) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(268,709,449) x common factors =1 x 1 = 1
LCM(268,709,449) = ( 268 × 709 × 449 ) / 1
LCM(268,709,449) = 85315388 / 1
LCM(268,709,449) = 85315388
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FAQs on GCF of Fractions of 86/268, 84/709, 315/449
1. What is the HCF of 86,84,315?
The HCF of 86,84,315 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 86/268, 84/709, 315/449?
Answer: GCF of Numerators as per given numbers 86/268, 84/709, 315/449 is
GCF of Numerators i.e. for 86,84,315 is 1
LCM of denominators i.e. for 268,709,449 is 85315388.
Thus, GCF of Fractions is 1/85315388.Finally, GCF of Fractions for 86/268, 84/709, 315/449 is 1/85315388.