GCF of 7228/342, 7910/7830
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7228/342, 7910/7830 i.e 2/148770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7228/342, 7910/7830.
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 7228/342,7910/7830?
Given fractions are 7228/342,7910/7830
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 7228/342,7910/7830, numerators are 7228,7910
Denominators are 342,7830
The GCF of 7228,7910 is 2 .
LCM of 342,7830 is 148770.
The greatest common factor of 7228/342,7910/7830 = [GCF of 7228,7910]/[LCM of 342,7830]= 2/148770
Therefore, the GCF of 7228/342,7910/7830 is 2/148770.
To find the highest common factor of 7228,7910, we have to find the factors of both numbers and list the highest common factor.
The factors of 7228 are 1, 2, 4, 13, 26, 52, 139, 278, 556, 1807, 3614, 7228
The factors of 7910 are 1, 2, 5, 7, 10, 14, 35, 70, 113, 226, 565, 791, 1130, 1582, 3955, 7910
The HCF of 7228,7910 is 2.
Lets's calculate GCF of 7228,7910
| 2 | 7228, 7910 |
| 3614, 3955 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7228,7910 By Matching Biggest Common Factor Method
Now, list down the factors of 7228
:1,2,4,13,26,52,139,278,556,1807,3614,7228
Now, list down the factors of 7910
:1,2,5,7,10,14,35,70,113,226,565,791,1130,1582,3955,7910
Greatest Common Factor
We found the factors 7228,7910 . The biggest common factor number is the GCF number.
So the greatest common factor 7228,7910 is 2.
Lets's calculate LCM of 342,7830
| 2 | 342, 7830 |
| 3 | 171, 3915 |
| 3 | 57, 1305 |
| 19, 435 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 19 x 435 = 148770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/148770
Therefore, the GCF of Fractions 7228/342,7910/7830 is 2/148770
Least Common Multiple of 342,7830 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 342,7830 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,7830) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(342,7830) x common factors =18 x 1 = 18
LCM(342,7830) = ( 342 × 7830 ) / 18
LCM(342,7830) = 2677860 / 18
LCM(342,7830) = 148770
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FAQs on GCF of Fractions of 7228/342, 7910/7830
1. What is the HCF of 7228,7910?
The HCF of 7228,7910 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 7228/342, 7910/7830?
Answer: GCF of Numerators as per given numbers 7228/342, 7910/7830 is
GCF of Numerators i.e. for 7228,7910 is 2
LCM of denominators i.e. for 342,7830 is 148770.
Thus, GCF of Fractions is 2/148770.Finally, GCF of Fractions for 7228/342, 7910/7830 is 2/148770.