GCF of 30/340, 64/266, 123/510
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/340, 64/266, 123/510 i.e 1/135660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/340, 64/266, 123/510.
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 30/340,64/266,123/510?
Given fractions are 30/340,64/266,123/510
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 30/340,64/266,123/510, numerators are 30,64,123
Denominators are 340,266,510
The GCF of 30,64,123 is 1 .
LCM of 340,266,510 is 135660.
The greatest common factor of 30/340,64/266,123/510 = [GCF of 30,64,123]/[LCM of 340,266,510]= 1/135660
Therefore, the GCF of 30/340,64/266,123/510 is 1/135660.
To find the highest common factor of 30,64,123, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 123 are 1, 3, 41, 123
The HCF of 30,64,123 is 1.
Lets's calculate GCF of 30,64,123
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 30,64,123 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 123
:1,3,41,123
Greatest Common Factor
We found the factors 30,64,123 . The biggest common factor number is the GCF number.
So the greatest common factor 30,64,123 is 1.
Lets's calculate LCM of 340,266,510
| 2 | 340, 266, 510 |
| 5 | 170, 133, 255 |
| 17 | 34, 133, 51 |
| 2, 133, 3 |
∴ So the LCM of the given numbers is 2 x 5 x 17 x 2 x 133 x 3 = 135660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/135660
Therefore, the GCF of Fractions 30/340,64/266,123/510 is 1/135660
Least Common Multiple of 340,266,510 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 340,266,510 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(340,266,510) = 2
common factors(in case of two or more numbers have common factors) = 170
GCF(340,266,510) x common factors =2 x 170 = 340
LCM(340,266,510) = ( 340 × 266 × 510 ) / 340
LCM(340,266,510) = 46124400 / 340
LCM(340,266,510) = 135660
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FAQs on GCF of Fractions of 30/340, 64/266, 123/510
1. What is the HCF of 30,64,123?
The HCF of 30,64,123 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 30/340, 64/266, 123/510?
Answer: GCF of Numerators as per given numbers 30/340, 64/266, 123/510 is
GCF of Numerators i.e. for 30,64,123 is 1
LCM of denominators i.e. for 340,266,510 is 135660.
Thus, GCF of Fractions is 1/135660.Finally, GCF of Fractions for 30/340, 64/266, 123/510 is 1/135660.