GCF of 28/16, 42/138, 282/667
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 28/16, 42/138, 282/667 i.e 2/32016 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/16, 42/138, 282/667.
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 28/16,42/138,282/667?
Given fractions are 28/16,42/138,282/667
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 28/16,42/138,282/667, numerators are 28,42,282
Denominators are 16,138,667
The GCF of 28,42,282 is 2 .
LCM of 16,138,667 is 32016.
The greatest common factor of 28/16,42/138,282/667 = [GCF of 28,42,282]/[LCM of 16,138,667]= 2/32016
Therefore, the GCF of 28/16,42/138,282/667 is 2/32016.
To find the highest common factor of 28,42,282, we have to find the factors of both numbers and list the highest common factor.
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282
The HCF of 28,42,282 is 2.
Lets's calculate GCF of 28,42,282
| 2 | 28, 42, 282 |
| 14, 21, 141 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 28,42,282 By Matching Biggest Common Factor Method
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 282
:1,2,3,6,47,94,141,282
Greatest Common Factor
We found the factors 28,42,282 . The biggest common factor number is the GCF number.
So the greatest common factor 28,42,282 is 2.
Lets's calculate LCM of 16,138,667
| 2 | 16, 138, 667 |
| 23 | 8, 69, 667 |
| 8, 3, 29 |
∴ So the LCM of the given numbers is 2 x 23 x 8 x 3 x 29 = 32016
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/32016
Therefore, the GCF of Fractions 28/16,42/138,282/667 is 2/32016
Least Common Multiple of 16,138,667 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 16,138,667 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,138,667) = 1
common factors(in case of two or more numbers have common factors) = 46
GCF(16,138,667) x common factors =1 x 46 = 46
LCM(16,138,667) = ( 16 × 138 × 667 ) / 46
LCM(16,138,667) = 1472736 / 46
LCM(16,138,667) = 32016
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FAQs on GCF of Fractions of 28/16, 42/138, 282/667
1. What is the HCF of 28,42,282?
The HCF of 28,42,282 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 28/16, 42/138, 282/667?
Answer: GCF of Numerators as per given numbers 28/16, 42/138, 282/667 is
GCF of Numerators i.e. for 28,42,282 is 2
LCM of denominators i.e. for 16,138,667 is 32016.
Thus, GCF of Fractions is 2/32016.Finally, GCF of Fractions for 28/16, 42/138, 282/667 is 2/32016.