GCF of 5110/429, 7315/7131
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5110/429, 7315/7131 i.e 35/1019733 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5110/429, 7315/7131.
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 5110/429,7315/7131?
Given fractions are 5110/429,7315/7131
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 5110/429,7315/7131, numerators are 5110,7315
Denominators are 429,7131
The GCF of 5110,7315 is 35 .
LCM of 429,7131 is 1019733.
The greatest common factor of 5110/429,7315/7131 = [GCF of 5110,7315]/[LCM of 429,7131]= 35/1019733
Therefore, the GCF of 5110/429,7315/7131 is 35/1019733.
To find the highest common factor of 5110,7315, we have to find the factors of both numbers and list the highest common factor.
The factors of 5110 are 1, 2, 5, 7, 10, 14, 35, 70, 73, 146, 365, 511, 730, 1022, 2555, 5110
The factors of 7315 are 1, 5, 7, 11, 19, 35, 55, 77, 95, 133, 209, 385, 665, 1045, 1463, 7315
The HCF of 5110,7315 is 35.
Lets's calculate GCF of 5110,7315
| 5 | 5110, 7315 |
| 7 | 1022, 1463 |
| 146, 209 |
∴ So the GCF of the given numbers is 5 x 7 = 35
Greatest Common Factor of 5110,7315 By Matching Biggest Common Factor Method
Now, list down the factors of 5110
:1,2,5,7,10,14,35,70,73,146,365,511,730,1022,2555,5110
Now, list down the factors of 7315
:1,5,7,11,19,35,55,77,95,133,209,385,665,1045,1463,7315
Greatest Common Factor
We found the factors 5110,7315 . The biggest common factor number is the GCF number.
So the greatest common factor 5110,7315 is 35.
Lets's calculate LCM of 429,7131
| 3 | 429, 7131 |
| 143, 2377 |
∴ So the LCM of the given numbers is 3 x 143 x 2377 = 1019733
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 35/1019733
Therefore, the GCF of Fractions 5110/429,7315/7131 is 35/1019733
Least Common Multiple of 429,7131 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 429,7131 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(429,7131) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(429,7131) x common factors =3 x 1 = 3
LCM(429,7131) = ( 429 × 7131 ) / 3
LCM(429,7131) = 3059199 / 3
LCM(429,7131) = 1019733
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FAQs on GCF of Fractions of 5110/429, 7315/7131
1. What is the HCF of 5110,7315?
The HCF of 5110,7315 is 35
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 5110/429, 7315/7131?
Answer: GCF of Numerators as per given numbers 5110/429, 7315/7131 is
GCF of Numerators i.e. for 5110,7315 is 35
LCM of denominators i.e. for 429,7131 is 1019733.
Thus, GCF of Fractions is 35/1019733.Finally, GCF of Fractions for 5110/429, 7315/7131 is 35/1019733.