GCF of 7678/274, 5304/4617
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7678/274, 5304/4617 i.e 2/1265058 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7678/274, 5304/4617.
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 7678/274,5304/4617?
Given fractions are 7678/274,5304/4617
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 7678/274,5304/4617, numerators are 7678,5304
Denominators are 274,4617
The GCF of 7678,5304 is 2 .
LCM of 274,4617 is 1265058.
The greatest common factor of 7678/274,5304/4617 = [GCF of 7678,5304]/[LCM of 274,4617]= 2/1265058
Therefore, the GCF of 7678/274,5304/4617 is 2/1265058.
To find the highest common factor of 7678,5304, we have to find the factors of both numbers and list the highest common factor.
The factors of 7678 are 1, 2, 11, 22, 349, 698, 3839, 7678
The factors of 5304 are 1, 2, 3, 4, 6, 8, 12, 13, 17, 24, 26, 34, 39, 51, 52, 68, 78, 102, 104, 136, 156, 204, 221, 312, 408, 442, 663, 884, 1326, 1768, 2652, 5304
The HCF of 7678,5304 is 2.
Lets's calculate GCF of 7678,5304
| 2 | 7678, 5304 |
| 3839, 2652 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7678,5304 By Matching Biggest Common Factor Method
Now, list down the factors of 7678
:1,2,11,22,349,698,3839,7678
Now, list down the factors of 5304
:1,2,3,4,6,8,12,13,17,24,26,34,39,51,52,68,78,102,104,136,156,204,221,312,408,442,663,884,1326,1768,2652,5304
Greatest Common Factor
We found the factors 7678,5304 . The biggest common factor number is the GCF number.
So the greatest common factor 7678,5304 is 2.
Lets's calculate LCM of 274,4617
Given numbers has no common factors except 1. So, there LCM is their product i.e 1265058
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1265058
Therefore, the GCF of Fractions 7678/274,5304/4617 is 2/1265058
Least Common Multiple of 274,4617 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 274,4617 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(274,4617) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(274,4617) x common factors =1 x 1 = 1
LCM(274,4617) = ( 274 × 4617 ) / 1
LCM(274,4617) = 1265058 / 1
LCM(274,4617) = 1265058
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FAQs on GCF of Fractions of 7678/274, 5304/4617
1. What is the HCF of 7678,5304?
The HCF of 7678,5304 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 7678/274, 5304/4617?
Answer: GCF of Numerators as per given numbers 7678/274, 5304/4617 is
GCF of Numerators i.e. for 7678,5304 is 2
LCM of denominators i.e. for 274,4617 is 1265058.
Thus, GCF of Fractions is 2/1265058.Finally, GCF of Fractions for 7678/274, 5304/4617 is 2/1265058.