GCF of 430/646, 514/318
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 430/646, 514/318 i.e 2/102714 easily. The following is the detailed procedure to determine the greatest common factor of fractions 430/646, 514/318.
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 430/646,514/318?
Given fractions are 430/646,514/318
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 430/646,514/318, numerators are 430,514
Denominators are 646,318
The GCF of 430,514 is 2 .
LCM of 646,318 is 102714.
The greatest common factor of 430/646,514/318 = [GCF of 430,514]/[LCM of 646,318]= 2/102714
Therefore, the GCF of 430/646,514/318 is 2/102714.
To find the highest common factor of 430,514, we have to find the factors of both numbers and list the highest common factor.
The factors of 430 are 1, 2, 5, 10, 43, 86, 215, 430
The factors of 514 are 1, 2, 257, 514
The HCF of 430,514 is 2.
Lets's calculate GCF of 430,514
| 2 | 430, 514 |
| 215, 257 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 430,514 By Matching Biggest Common Factor Method
Now, list down the factors of 430
:1,2,5,10,43,86,215,430
Now, list down the factors of 514
:1,2,257,514
Greatest Common Factor
We found the factors 430,514 . The biggest common factor number is the GCF number.
So the greatest common factor 430,514 is 2.
Lets's calculate LCM of 646,318
| 2 | 646, 318 |
| 323, 159 |
∴ So the LCM of the given numbers is 2 x 323 x 159 = 102714
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/102714
Therefore, the GCF of Fractions 430/646,514/318 is 2/102714
Least Common Multiple of 646,318 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 646,318 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(646,318) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(646,318) x common factors =2 x 1 = 2
LCM(646,318) = ( 646 × 318 ) / 2
LCM(646,318) = 205428 / 2
LCM(646,318) = 102714
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FAQs on GCF of Fractions of 430/646, 514/318
1. What is the HCF of 430,514?
The HCF of 430,514 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 430/646, 514/318?
Answer: GCF of Numerators as per given numbers 430/646, 514/318 is
GCF of Numerators i.e. for 430,514 is 2
LCM of denominators i.e. for 646,318 is 102714.
Thus, GCF of Fractions is 2/102714.Finally, GCF of Fractions for 430/646, 514/318 is 2/102714.