GCF of 360/209, 8360/7714
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 360/209, 8360/7714 i.e 40/84854 easily. The following is the detailed procedure to determine the greatest common factor of fractions 360/209, 8360/7714.
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 360/209,8360/7714?
Given fractions are 360/209,8360/7714
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 360/209,8360/7714, numerators are 360,8360
Denominators are 209,7714
The GCF of 360,8360 is 40 .
LCM of 209,7714 is 84854.
The greatest common factor of 360/209,8360/7714 = [GCF of 360,8360]/[LCM of 209,7714]= 40/84854
Therefore, the GCF of 360/209,8360/7714 is 40/84854.
To find the highest common factor of 360,8360, we have to find the factors of both numbers and list the highest common factor.
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The factors of 8360 are 1, 2, 4, 5, 8, 10, 11, 19, 20, 22, 38, 40, 44, 55, 76, 88, 95, 110, 152, 190, 209, 220, 380, 418, 440, 760, 836, 1045, 1672, 2090, 4180, 8360
The HCF of 360,8360 is 40.
Lets's calculate GCF of 360,8360
| 2 | 360, 8360 |
| 2 | 180, 4180 |
| 2 | 90, 2090 |
| 5 | 45, 1045 |
| 9, 209 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Greatest Common Factor of 360,8360 By Matching Biggest Common Factor Method
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Now, list down the factors of 8360
:1,2,4,5,8,10,11,19,20,22,38,40,44,55,76,88,95,110,152,190,209,220,380,418,440,760,836,1045,1672,2090,4180,8360
Greatest Common Factor
We found the factors 360,8360 . The biggest common factor number is the GCF number.
So the greatest common factor 360,8360 is 40.
Lets's calculate LCM of 209,7714
| 19 | 209, 7714 |
| 11, 406 |
∴ So the LCM of the given numbers is 19 x 11 x 406 = 84854
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/84854
Therefore, the GCF of Fractions 360/209,8360/7714 is 40/84854
Least Common Multiple of 209,7714 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 209,7714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(209,7714) = 19
common factors(in case of two or more numbers have common factors) = 1
GCF(209,7714) x common factors =19 x 1 = 19
LCM(209,7714) = ( 209 × 7714 ) / 19
LCM(209,7714) = 1612226 / 19
LCM(209,7714) = 84854
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FAQs on GCF of Fractions of 360/209, 8360/7714
1. What is the HCF of 360,8360?
The HCF of 360,8360 is 40
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 360/209, 8360/7714?
Answer: GCF of Numerators as per given numbers 360/209, 8360/7714 is
GCF of Numerators i.e. for 360,8360 is 40
LCM of denominators i.e. for 209,7714 is 84854.
Thus, GCF of Fractions is 40/84854.Finally, GCF of Fractions for 360/209, 8360/7714 is 40/84854.