GCF of 35/48, 84/38, 282/319
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 35/48, 84/38, 282/319 i.e 1/290928 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/48, 84/38, 282/319.
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 35/48,84/38,282/319?
Given fractions are 35/48,84/38,282/319
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 35/48,84/38,282/319, numerators are 35,84,282
Denominators are 48,38,319
The GCF of 35,84,282 is 1 .
LCM of 48,38,319 is 290928.
The greatest common factor of 35/48,84/38,282/319 = [GCF of 35,84,282]/[LCM of 48,38,319]= 1/290928
Therefore, the GCF of 35/48,84/38,282/319 is 1/290928.
To find the highest common factor of 35,84,282, we have to find the factors of both numbers and list the highest common factor.
The factors of 35 are 1, 5, 7, 35
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282
The HCF of 35,84,282 is 1.
Lets's calculate GCF of 35,84,282
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 35,84,282 By Matching Biggest Common Factor Method
Now, list down the factors of 35
:1,5,7,35
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 282
:1,2,3,6,47,94,141,282
Greatest Common Factor
We found the factors 35,84,282 . The biggest common factor number is the GCF number.
So the greatest common factor 35,84,282 is 1.
Lets's calculate LCM of 48,38,319
| 2 | 48, 38, 319 |
| 24, 19, 319 |
∴ So the LCM of the given numbers is 2 x 24 x 19 x 319 = 290928
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/290928
Therefore, the GCF of Fractions 35/48,84/38,282/319 is 1/290928
Least Common Multiple of 48,38,319 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 48,38,319 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(48,38,319) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(48,38,319) x common factors =1 x 2 = 2
LCM(48,38,319) = ( 48 × 38 × 319 ) / 2
LCM(48,38,319) = 581856 / 2
LCM(48,38,319) = 290928
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FAQs on GCF of Fractions of 35/48, 84/38, 282/319
1. What is the HCF of 35,84,282?
The HCF of 35,84,282 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 35/48, 84/38, 282/319?
Answer: GCF of Numerators as per given numbers 35/48, 84/38, 282/319 is
GCF of Numerators i.e. for 35,84,282 is 1
LCM of denominators i.e. for 48,38,319 is 290928.
Thus, GCF of Fractions is 1/290928.Finally, GCF of Fractions for 35/48, 84/38, 282/319 is 1/290928.