GCF of 8076/205, 9189/9714
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8076/205, 9189/9714 i.e 3/1991370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8076/205, 9189/9714.
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 8076/205,9189/9714?
Given fractions are 8076/205,9189/9714
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 8076/205,9189/9714, numerators are 8076,9189
Denominators are 205,9714
The GCF of 8076,9189 is 3 .
LCM of 205,9714 is 1991370.
The greatest common factor of 8076/205,9189/9714 = [GCF of 8076,9189]/[LCM of 205,9714]= 3/1991370
Therefore, the GCF of 8076/205,9189/9714 is 3/1991370.
To find the highest common factor of 8076,9189, we have to find the factors of both numbers and list the highest common factor.
The factors of 8076 are 1, 2, 3, 4, 6, 12, 673, 1346, 2019, 2692, 4038, 8076
The factors of 9189 are 1, 3, 9, 1021, 3063, 9189
The HCF of 8076,9189 is 3.
Lets's calculate GCF of 8076,9189
| 3 | 8076, 9189 |
| 2692, 3063 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 8076,9189 By Matching Biggest Common Factor Method
Now, list down the factors of 8076
:1,2,3,4,6,12,673,1346,2019,2692,4038,8076
Now, list down the factors of 9189
:1,3,9,1021,3063,9189
Greatest Common Factor
We found the factors 8076,9189 . The biggest common factor number is the GCF number.
So the greatest common factor 8076,9189 is 3.
Lets's calculate LCM of 205,9714
Given numbers has no common factors except 1. So, there LCM is their product i.e 1991370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1991370
Therefore, the GCF of Fractions 8076/205,9189/9714 is 3/1991370
Least Common Multiple of 205,9714 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 205,9714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,9714) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,9714) x common factors =1 x 1 = 1
LCM(205,9714) = ( 205 × 9714 ) / 1
LCM(205,9714) = 1991370 / 1
LCM(205,9714) = 1991370
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FAQs on GCF of Fractions of 8076/205, 9189/9714
1. What is the HCF of 8076,9189?
The HCF of 8076,9189 is 3
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 8076/205, 9189/9714?
Answer: GCF of Numerators as per given numbers 8076/205, 9189/9714 is
GCF of Numerators i.e. for 8076,9189 is 3
LCM of denominators i.e. for 205,9714 is 1991370.
Thus, GCF of Fractions is 3/1991370.Finally, GCF of Fractions for 8076/205, 9189/9714 is 3/1991370.