GCF of 430/616, 560/354
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 430/616, 560/354 i.e 10/109032 easily. The following is the detailed procedure to determine the greatest common factor of fractions 430/616, 560/354.
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 430/616,560/354?
Given fractions are 430/616,560/354
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 430/616,560/354, numerators are 430,560
Denominators are 616,354
The GCF of 430,560 is 10 .
LCM of 616,354 is 109032.
The greatest common factor of 430/616,560/354 = [GCF of 430,560]/[LCM of 616,354]= 10/109032
Therefore, the GCF of 430/616,560/354 is 10/109032.
To find the highest common factor of 430,560, 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 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The HCF of 430,560 is 10.
Lets's calculate GCF of 430,560
| 2 | 430, 560 |
| 5 | 215, 280 |
| 43, 56 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 430,560 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 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Greatest Common Factor
We found the factors 430,560 . The biggest common factor number is the GCF number.
So the greatest common factor 430,560 is 10.
Lets's calculate LCM of 616,354
| 2 | 616, 354 |
| 308, 177 |
∴ So the LCM of the given numbers is 2 x 308 x 177 = 109032
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/109032
Therefore, the GCF of Fractions 430/616,560/354 is 10/109032
Least Common Multiple of 616,354 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 616,354 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(616,354) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(616,354) x common factors =2 x 1 = 2
LCM(616,354) = ( 616 × 354 ) / 2
LCM(616,354) = 218064 / 2
LCM(616,354) = 109032
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FAQs on GCF of Fractions of 430/616, 560/354
1. What is the HCF of 430,560?
The HCF of 430,560 is 10
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 430/616, 560/354?
Answer: GCF of Numerators as per given numbers 430/616, 560/354 is
GCF of Numerators i.e. for 430,560 is 10
LCM of denominators i.e. for 616,354 is 109032.
Thus, GCF of Fractions is 10/109032.Finally, GCF of Fractions for 430/616, 560/354 is 10/109032.