GCF of 730/390, 7722/129
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 730/390, 7722/129 i.e 2/16770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 730/390, 7722/129.
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 730/390,7722/129?
Given fractions are 730/390,7722/129
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 730/390,7722/129, numerators are 730,7722
Denominators are 390,129
The GCF of 730,7722 is 2 .
LCM of 390,129 is 16770.
The greatest common factor of 730/390,7722/129 = [GCF of 730,7722]/[LCM of 390,129]= 2/16770
Therefore, the GCF of 730/390,7722/129 is 2/16770.
To find the highest common factor of 730,7722, we have to find the factors of both numbers and list the highest common factor.
The factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730
The factors of 7722 are 1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 27, 33, 39, 54, 66, 78, 99, 117, 143, 198, 234, 286, 297, 351, 429, 594, 702, 858, 1287, 2574, 3861, 7722
The HCF of 730,7722 is 2.
Lets's calculate GCF of 730,7722
| 2 | 730, 7722 |
| 365, 3861 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 730,7722 By Matching Biggest Common Factor Method
Now, list down the factors of 730
:1,2,5,10,73,146,365,730
Now, list down the factors of 7722
:1,2,3,6,9,11,13,18,22,26,27,33,39,54,66,78,99,117,143,198,234,286,297,351,429,594,702,858,1287,2574,3861,7722
Greatest Common Factor
We found the factors 730,7722 . The biggest common factor number is the GCF number.
So the greatest common factor 730,7722 is 2.
Lets's calculate LCM of 390,129
| 3 | 390, 129 |
| 130, 43 |
∴ So the LCM of the given numbers is 3 x 130 x 43 = 16770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/16770
Therefore, the GCF of Fractions 730/390,7722/129 is 2/16770
Least Common Multiple of 390,129 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 390,129 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(390,129) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(390,129) x common factors =3 x 1 = 3
LCM(390,129) = ( 390 × 129 ) / 3
LCM(390,129) = 50310 / 3
LCM(390,129) = 16770
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FAQs on GCF of Fractions of 730/390, 7722/129
1. What is the HCF of 730,7722?
The HCF of 730,7722 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 730/390, 7722/129?
Answer: GCF of Numerators as per given numbers 730/390, 7722/129 is
GCF of Numerators i.e. for 730,7722 is 2
LCM of denominators i.e. for 390,129 is 16770.
Thus, GCF of Fractions is 2/16770.Finally, GCF of Fractions for 730/390, 7722/129 is 2/16770.