GCF of 5404/120, 7098/8345
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5404/120, 7098/8345 i.e 14/200280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5404/120, 7098/8345.
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 5404/120,7098/8345?
Given fractions are 5404/120,7098/8345
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 5404/120,7098/8345, numerators are 5404,7098
Denominators are 120,8345
The GCF of 5404,7098 is 14 .
LCM of 120,8345 is 200280.
The greatest common factor of 5404/120,7098/8345 = [GCF of 5404,7098]/[LCM of 120,8345]= 14/200280
Therefore, the GCF of 5404/120,7098/8345 is 14/200280.
To find the highest common factor of 5404,7098, we have to find the factors of both numbers and list the highest common factor.
The factors of 5404 are 1, 2, 4, 7, 14, 28, 193, 386, 772, 1351, 2702, 5404
The factors of 7098 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 169, 182, 273, 338, 507, 546, 1014, 1183, 2366, 3549, 7098
The HCF of 5404,7098 is 14.
Lets's calculate GCF of 5404,7098
| 2 | 5404, 7098 |
| 7 | 2702, 3549 |
| 386, 507 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 5404,7098 By Matching Biggest Common Factor Method
Now, list down the factors of 5404
:1,2,4,7,14,28,193,386,772,1351,2702,5404
Now, list down the factors of 7098
:1,2,3,6,7,13,14,21,26,39,42,78,91,169,182,273,338,507,546,1014,1183,2366,3549,7098
Greatest Common Factor
We found the factors 5404,7098 . The biggest common factor number is the GCF number.
So the greatest common factor 5404,7098 is 14.
Lets's calculate LCM of 120,8345
| 5 | 120, 8345 |
| 24, 1669 |
∴ So the LCM of the given numbers is 5 x 24 x 1669 = 200280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/200280
Therefore, the GCF of Fractions 5404/120,7098/8345 is 14/200280
Least Common Multiple of 120,8345 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 120,8345 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(120,8345) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(120,8345) x common factors =5 x 1 = 5
LCM(120,8345) = ( 120 × 8345 ) / 5
LCM(120,8345) = 1001400 / 5
LCM(120,8345) = 200280
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FAQs on GCF of Fractions of 5404/120, 7098/8345
1. What is the HCF of 5404,7098?
The HCF of 5404,7098 is 14
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 5404/120, 7098/8345?
Answer: GCF of Numerators as per given numbers 5404/120, 7098/8345 is
GCF of Numerators i.e. for 5404,7098 is 14
LCM of denominators i.e. for 120,8345 is 200280.
Thus, GCF of Fractions is 14/200280.Finally, GCF of Fractions for 5404/120, 7098/8345 is 14/200280.