GCF of 470/856, 320/284
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 470/856, 320/284 i.e 10/60776 easily. The following is the detailed procedure to determine the greatest common factor of fractions 470/856, 320/284.
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 470/856,320/284?
Given fractions are 470/856,320/284
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 470/856,320/284, numerators are 470,320
Denominators are 856,284
The GCF of 470,320 is 10 .
LCM of 856,284 is 60776.
The greatest common factor of 470/856,320/284 = [GCF of 470,320]/[LCM of 856,284]= 10/60776
Therefore, the GCF of 470/856,320/284 is 10/60776.
To find the highest common factor of 470,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 470,320 is 10.
Lets's calculate GCF of 470,320
| 2 | 470, 320 |
| 5 | 235, 160 |
| 47, 32 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 470,320 By Matching Biggest Common Factor Method
Now, list down the factors of 470
:1,2,5,10,47,94,235,470
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 470,320 . The biggest common factor number is the GCF number.
So the greatest common factor 470,320 is 10.
Lets's calculate LCM of 856,284
| 2 | 856, 284 |
| 2 | 428, 142 |
| 214, 71 |
∴ So the LCM of the given numbers is 2 x 2 x 214 x 71 = 60776
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/60776
Therefore, the GCF of Fractions 470/856,320/284 is 10/60776
Least Common Multiple of 856,284 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 856,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(856,284) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(856,284) x common factors =4 x 1 = 4
LCM(856,284) = ( 856 × 284 ) / 4
LCM(856,284) = 243104 / 4
LCM(856,284) = 60776
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FAQs on GCF of Fractions of 470/856, 320/284
1. What is the HCF of 470,320?
The HCF of 470,320 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 470/856, 320/284?
Answer: GCF of Numerators as per given numbers 470/856, 320/284 is
GCF of Numerators i.e. for 470,320 is 10
LCM of denominators i.e. for 856,284 is 60776.
Thus, GCF of Fractions is 10/60776.Finally, GCF of Fractions for 470/856, 320/284 is 10/60776.