GCF of 7424/205, 8766/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7424/205, 8766/678 i.e 2/138990 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7424/205, 8766/678.
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 7424/205,8766/678?
Given fractions are 7424/205,8766/678
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 7424/205,8766/678, numerators are 7424,8766
Denominators are 205,678
The GCF of 7424,8766 is 2 .
LCM of 205,678 is 138990.
The greatest common factor of 7424/205,8766/678 = [GCF of 7424,8766]/[LCM of 205,678]= 2/138990
Therefore, the GCF of 7424/205,8766/678 is 2/138990.
To find the highest common factor of 7424,8766, we have to find the factors of both numbers and list the highest common factor.
The factors of 7424 are 1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 128, 232, 256, 464, 928, 1856, 3712, 7424
The factors of 8766 are 1, 2, 3, 6, 9, 18, 487, 974, 1461, 2922, 4383, 8766
The HCF of 7424,8766 is 2.
Lets's calculate GCF of 7424,8766
| 2 | 7424, 8766 |
| 3712, 4383 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7424,8766 By Matching Biggest Common Factor Method
Now, list down the factors of 7424
:1,2,4,8,16,29,32,58,64,116,128,232,256,464,928,1856,3712,7424
Now, list down the factors of 8766
:1,2,3,6,9,18,487,974,1461,2922,4383,8766
Greatest Common Factor
We found the factors 7424,8766 . The biggest common factor number is the GCF number.
So the greatest common factor 7424,8766 is 2.
Lets's calculate LCM of 205,678
Given numbers has no common factors except 1. So, there LCM is their product i.e 138990
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/138990
Therefore, the GCF of Fractions 7424/205,8766/678 is 2/138990
Least Common Multiple of 205,678 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 205,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,678) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,678) x common factors =1 x 1 = 1
LCM(205,678) = ( 205 × 678 ) / 1
LCM(205,678) = 138990 / 1
LCM(205,678) = 138990
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FAQs on GCF of Fractions of 7424/205, 8766/678
1. What is the HCF of 7424,8766?
The HCF of 7424,8766 is 2
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 7424/205, 8766/678?
Answer: GCF of Numerators as per given numbers 7424/205, 8766/678 is
GCF of Numerators i.e. for 7424,8766 is 2
LCM of denominators i.e. for 205,678 is 138990.
Thus, GCF of Fractions is 2/138990.Finally, GCF of Fractions for 7424/205, 8766/678 is 2/138990.