GCF of 268/76, 128/13, 399/30
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 268/76, 128/13, 399/30 i.e 1/14820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 268/76, 128/13, 399/30.
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 268/76,128/13,399/30?
Given fractions are 268/76,128/13,399/30
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 268/76,128/13,399/30, numerators are 268,128,399
Denominators are 76,13,30
The GCF of 268,128,399 is 1 .
LCM of 76,13,30 is 14820.
The greatest common factor of 268/76,128/13,399/30 = [GCF of 268,128,399]/[LCM of 76,13,30]= 1/14820
Therefore, the GCF of 268/76,128/13,399/30 is 1/14820.
To find the highest common factor of 268,128,399, we have to find the factors of both numbers and list the highest common factor.
The factors of 268 are 1, 2, 4, 67, 134, 268
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
The factors of 399 are 1, 3, 7, 19, 21, 57, 133, 399
The HCF of 268,128,399 is 1.
Lets's calculate GCF of 268,128,399
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 268,128,399 By Matching Biggest Common Factor Method
Now, list down the factors of 268
:1,2,4,67,134,268
Now, list down the factors of 128
:1,2,4,8,16,32,64,128
Now, list down the factors of 399
:1,3,7,19,21,57,133,399
Greatest Common Factor
We found the factors 268,128,399 . The biggest common factor number is the GCF number.
So the greatest common factor 268,128,399 is 1.
Lets's calculate LCM of 76,13,30
| 2 | 76, 13, 30 |
| 38, 13, 15 |
∴ So the LCM of the given numbers is 2 x 38 x 13 x 15 = 14820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14820
Therefore, the GCF of Fractions 268/76,128/13,399/30 is 1/14820
Least Common Multiple of 76,13,30 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 76,13,30 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,13,30) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(76,13,30) x common factors =1 x 2 = 2
LCM(76,13,30) = ( 76 × 13 × 30 ) / 2
LCM(76,13,30) = 29640 / 2
LCM(76,13,30) = 14820
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FAQs on GCF of Fractions of 268/76, 128/13, 399/30
1. What is the HCF of 268,128,399?
The HCF of 268,128,399 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 268/76, 128/13, 399/30?
Answer: GCF of Numerators as per given numbers 268/76, 128/13, 399/30 is
GCF of Numerators i.e. for 268,128,399 is 1
LCM of denominators i.e. for 76,13,30 is 14820.
Thus, GCF of Fractions is 1/14820.Finally, GCF of Fractions for 268/76, 128/13, 399/30 is 1/14820.