GCF of 14/26, 22/258, 512/182
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 14/26, 22/258, 512/182 i.e 2/23478 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/26, 22/258, 512/182.
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 14/26,22/258,512/182?
Given fractions are 14/26,22/258,512/182
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 14/26,22/258,512/182, numerators are 14,22,512
Denominators are 26,258,182
The GCF of 14,22,512 is 2 .
LCM of 26,258,182 is 23478.
The greatest common factor of 14/26,22/258,512/182 = [GCF of 14,22,512]/[LCM of 26,258,182]= 2/23478
Therefore, the GCF of 14/26,22/258,512/182 is 2/23478.
To find the highest common factor of 14,22,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 22 are 1, 2, 11, 22
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 14,22,512 is 2.
Lets's calculate GCF of 14,22,512
| 2 | 14, 22, 512 |
| 7, 11, 256 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 14,22,512 By Matching Biggest Common Factor Method
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 22
:1,2,11,22
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 14,22,512 . The biggest common factor number is the GCF number.
So the greatest common factor 14,22,512 is 2.
Lets's calculate LCM of 26,258,182
| 2 | 26, 258, 182 |
| 13 | 13, 129, 91 |
| 1, 129, 7 |
∴ So the LCM of the given numbers is 2 x 13 x 1 x 129 x 7 = 23478
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/23478
Therefore, the GCF of Fractions 14/26,22/258,512/182 is 2/23478
Least Common Multiple of 26,258,182 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 26,258,182 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(26,258,182) = 2
common factors(in case of two or more numbers have common factors) = 26
GCF(26,258,182) x common factors =2 x 26 = 52
LCM(26,258,182) = ( 26 × 258 × 182 ) / 52
LCM(26,258,182) = 1220856 / 52
LCM(26,258,182) = 23478
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FAQs on GCF of Fractions of 14/26, 22/258, 512/182
1. What is the HCF of 14,22,512?
The HCF of 14,22,512 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 14/26, 22/258, 512/182?
Answer: GCF of Numerators as per given numbers 14/26, 22/258, 512/182 is
GCF of Numerators i.e. for 14,22,512 is 2
LCM of denominators i.e. for 26,258,182 is 23478.
Thus, GCF of Fractions is 2/23478.Finally, GCF of Fractions for 14/26, 22/258, 512/182 is 2/23478.