GCF of 29/321, 54/700, 105/764
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 29/321, 54/700, 105/764 i.e 1/42917700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 29/321, 54/700, 105/764.
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 29/321,54/700,105/764?
Given fractions are 29/321,54/700,105/764
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 29/321,54/700,105/764, numerators are 29,54,105
Denominators are 321,700,764
The GCF of 29,54,105 is 1 .
LCM of 321,700,764 is 42917700.
The greatest common factor of 29/321,54/700,105/764 = [GCF of 29,54,105]/[LCM of 321,700,764]= 1/42917700
Therefore, the GCF of 29/321,54/700,105/764 is 1/42917700.
To find the highest common factor of 29,54,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 29 are 1, 29
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 29,54,105 is 1.
Lets's calculate GCF of 29,54,105
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 29,54,105 By Matching Biggest Common Factor Method
Now, list down the factors of 29
:1,29
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 29,54,105 . The biggest common factor number is the GCF number.
So the greatest common factor 29,54,105 is 1.
Lets's calculate LCM of 321,700,764
| 2 | 321, 700, 764 |
| 2 | 321, 350, 382 |
| 321, 175, 191 |
∴ So the LCM of the given numbers is 2 x 2 x 321 x 175 x 191 = 42917700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/42917700
Therefore, the GCF of Fractions 29/321,54/700,105/764 is 1/42917700
Least Common Multiple of 321,700,764 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 321,700,764 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(321,700,764) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(321,700,764) x common factors =1 x 4 = 4
LCM(321,700,764) = ( 321 × 700 × 764 ) / 4
LCM(321,700,764) = 171670800 / 4
LCM(321,700,764) = 42917700
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FAQs on GCF of Fractions of 29/321, 54/700, 105/764
1. What is the HCF of 29,54,105?
The HCF of 29,54,105 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 29/321, 54/700, 105/764?
Answer: GCF of Numerators as per given numbers 29/321, 54/700, 105/764 is
GCF of Numerators i.e. for 29,54,105 is 1
LCM of denominators i.e. for 321,700,764 is 42917700.
Thus, GCF of Fractions is 1/42917700.Finally, GCF of Fractions for 29/321, 54/700, 105/764 is 1/42917700.