GCF of 5584/421, 7678/7436
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5584/421, 7678/7436 i.e 698/3130556 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5584/421, 7678/7436.
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 5584/421,7678/7436?
Given fractions are 5584/421,7678/7436
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 5584/421,7678/7436, numerators are 5584,7678
Denominators are 421,7436
The GCF of 5584,7678 is 698 .
LCM of 421,7436 is 3130556.
The greatest common factor of 5584/421,7678/7436 = [GCF of 5584,7678]/[LCM of 421,7436]= 698/3130556
Therefore, the GCF of 5584/421,7678/7436 is 698/3130556.
To find the highest common factor of 5584,7678, we have to find the factors of both numbers and list the highest common factor.
The factors of 5584 are 1, 2, 4, 8, 16, 349, 698, 1396, 2792, 5584
The factors of 7678 are 1, 2, 11, 22, 349, 698, 3839, 7678
The HCF of 5584,7678 is 698.
Lets's calculate GCF of 5584,7678
| 2 | 5584, 7678 |
| 349 | 2792, 3839 |
| 8, 11 |
∴ So the GCF of the given numbers is 2 x 349 = 698
Greatest Common Factor of 5584,7678 By Matching Biggest Common Factor Method
Now, list down the factors of 5584
:1,2,4,8,16,349,698,1396,2792,5584
Now, list down the factors of 7678
:1,2,11,22,349,698,3839,7678
Greatest Common Factor
We found the factors 5584,7678 . The biggest common factor number is the GCF number.
So the greatest common factor 5584,7678 is 698.
Lets's calculate LCM of 421,7436
Given numbers has no common factors except 1. So, there LCM is their product i.e 3130556
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 698/3130556
Therefore, the GCF of Fractions 5584/421,7678/7436 is 698/3130556
Least Common Multiple of 421,7436 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 421,7436 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(421,7436) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(421,7436) x common factors =1 x 1 = 1
LCM(421,7436) = ( 421 × 7436 ) / 1
LCM(421,7436) = 3130556 / 1
LCM(421,7436) = 3130556
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FAQs on GCF of Fractions of 5584/421, 7678/7436
1. What is the HCF of 5584,7678?
The HCF of 5584,7678 is 698
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 5584/421, 7678/7436?
Answer: GCF of Numerators as per given numbers 5584/421, 7678/7436 is
GCF of Numerators i.e. for 5584,7678 is 698
LCM of denominators i.e. for 421,7436 is 3130556.
Thus, GCF of Fractions is 698/3130556.Finally, GCF of Fractions for 5584/421, 7678/7436 is 698/3130556.