GCF of 26/129, 61/430, 546/735
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 26/129, 61/430, 546/735 i.e 1/63210 easily. The following is the detailed procedure to determine the greatest common factor of fractions 26/129, 61/430, 546/735.
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 26/129,61/430,546/735?
Given fractions are 26/129,61/430,546/735
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 26/129,61/430,546/735, numerators are 26,61,546
Denominators are 129,430,735
The GCF of 26,61,546 is 1 .
LCM of 129,430,735 is 63210.
The greatest common factor of 26/129,61/430,546/735 = [GCF of 26,61,546]/[LCM of 129,430,735]= 1/63210
Therefore, the GCF of 26/129,61/430,546/735 is 1/63210.
To find the highest common factor of 26,61,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 26 are 1, 2, 13, 26
The factors of 61 are 1, 61
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 26,61,546 is 1.
Lets's calculate GCF of 26,61,546
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 26,61,546 By Matching Biggest Common Factor Method
Now, list down the factors of 26
:1,2,13,26
Now, list down the factors of 61
:1,61
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Greatest Common Factor
We found the factors 26,61,546 . The biggest common factor number is the GCF number.
So the greatest common factor 26,61,546 is 1.
Lets's calculate LCM of 129,430,735
| 3 | 129, 430, 735 |
| 5 | 43, 430, 245 |
| 43 | 43, 86, 49 |
| 1, 2, 49 |
∴ So the LCM of the given numbers is 3 x 5 x 43 x 1 x 2 x 49 = 63210
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/63210
Therefore, the GCF of Fractions 26/129,61/430,546/735 is 1/63210
Least Common Multiple of 129,430,735 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 129,430,735 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(129,430,735) = 1
common factors(in case of two or more numbers have common factors) = 645
GCF(129,430,735) x common factors =1 x 645 = 645
LCM(129,430,735) = ( 129 × 430 × 735 ) / 645
LCM(129,430,735) = 40770450 / 645
LCM(129,430,735) = 63210
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FAQs on GCF of Fractions of 26/129, 61/430, 546/735
1. What is the HCF of 26,61,546?
The HCF of 26,61,546 is 1
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 26/129, 61/430, 546/735?
Answer: GCF of Numerators as per given numbers 26/129, 61/430, 546/735 is
GCF of Numerators i.e. for 26,61,546 is 1
LCM of denominators i.e. for 129,430,735 is 63210.
Thus, GCF of Fractions is 1/63210.Finally, GCF of Fractions for 26/129, 61/430, 546/735 is 1/63210.