GCF of 7544/614, 8678/7032
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7544/614, 8678/7032 i.e 2/2158824 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7544/614, 8678/7032.
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 7544/614,8678/7032?
Given fractions are 7544/614,8678/7032
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 7544/614,8678/7032, numerators are 7544,8678
Denominators are 614,7032
The GCF of 7544,8678 is 2 .
LCM of 614,7032 is 2158824.
The greatest common factor of 7544/614,8678/7032 = [GCF of 7544,8678]/[LCM of 614,7032]= 2/2158824
Therefore, the GCF of 7544/614,8678/7032 is 2/2158824.
To find the highest common factor of 7544,8678, we have to find the factors of both numbers and list the highest common factor.
The factors of 7544 are 1, 2, 4, 8, 23, 41, 46, 82, 92, 164, 184, 328, 943, 1886, 3772, 7544
The factors of 8678 are 1, 2, 4339, 8678
The HCF of 7544,8678 is 2.
Lets's calculate GCF of 7544,8678
| 2 | 7544, 8678 |
| 3772, 4339 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7544,8678 By Matching Biggest Common Factor Method
Now, list down the factors of 7544
:1,2,4,8,23,41,46,82,92,164,184,328,943,1886,3772,7544
Now, list down the factors of 8678
:1,2,4339,8678
Greatest Common Factor
We found the factors 7544,8678 . The biggest common factor number is the GCF number.
So the greatest common factor 7544,8678 is 2.
Lets's calculate LCM of 614,7032
| 2 | 614, 7032 |
| 307, 3516 |
∴ So the LCM of the given numbers is 2 x 307 x 3516 = 2158824
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2158824
Therefore, the GCF of Fractions 7544/614,8678/7032 is 2/2158824
Least Common Multiple of 614,7032 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 614,7032 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(614,7032) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(614,7032) x common factors =2 x 1 = 2
LCM(614,7032) = ( 614 × 7032 ) / 2
LCM(614,7032) = 4317648 / 2
LCM(614,7032) = 2158824
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FAQs on GCF of Fractions of 7544/614, 8678/7032
1. What is the HCF of 7544,8678?
The HCF of 7544,8678 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 7544/614, 8678/7032?
Answer: GCF of Numerators as per given numbers 7544/614, 8678/7032 is
GCF of Numerators i.e. for 7544,8678 is 2
LCM of denominators i.e. for 614,7032 is 2158824.
Thus, GCF of Fractions is 2/2158824.Finally, GCF of Fractions for 7544/614, 8678/7032 is 2/2158824.