GCF of 320/259, 8216/370
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 320/259, 8216/370 i.e 8/2590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 320/259, 8216/370.
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 320/259,8216/370?
Given fractions are 320/259,8216/370
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 320/259,8216/370, numerators are 320,8216
Denominators are 259,370
The GCF of 320,8216 is 8 .
LCM of 259,370 is 2590.
The greatest common factor of 320/259,8216/370 = [GCF of 320,8216]/[LCM of 259,370]= 8/2590
Therefore, the GCF of 320/259,8216/370 is 8/2590.
To find the highest common factor of 320,8216, we have to find the factors of both numbers and list the highest common factor.
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The factors of 8216 are 1, 2, 4, 8, 13, 26, 52, 79, 104, 158, 316, 632, 1027, 2054, 4108, 8216
The HCF of 320,8216 is 8.
Lets's calculate GCF of 320,8216
| 2 | 320, 8216 |
| 2 | 160, 4108 |
| 2 | 80, 2054 |
| 40, 1027 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 320,8216 By Matching Biggest Common Factor Method
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Now, list down the factors of 8216
:1,2,4,8,13,26,52,79,104,158,316,632,1027,2054,4108,8216
Greatest Common Factor
We found the factors 320,8216 . The biggest common factor number is the GCF number.
So the greatest common factor 320,8216 is 8.
Lets's calculate LCM of 259,370
| 37 | 259, 370 |
| 7, 10 |
∴ So the LCM of the given numbers is 37 x 7 x 10 = 2590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/2590
Therefore, the GCF of Fractions 320/259,8216/370 is 8/2590
Least Common Multiple of 259,370 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 259,370 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(259,370) = 37
common factors(in case of two or more numbers have common factors) = 1
GCF(259,370) x common factors =37 x 1 = 37
LCM(259,370) = ( 259 × 370 ) / 37
LCM(259,370) = 95830 / 37
LCM(259,370) = 2590
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FAQs on GCF of Fractions of 320/259, 8216/370
1. What is the HCF of 320,8216?
The HCF of 320,8216 is 8
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 320/259, 8216/370?
Answer: GCF of Numerators as per given numbers 320/259, 8216/370 is
GCF of Numerators i.e. for 320,8216 is 8
LCM of denominators i.e. for 259,370 is 2590.
Thus, GCF of Fractions is 8/2590.Finally, GCF of Fractions for 320/259, 8216/370 is 8/2590.