GCF of 34/260, 21/330, 742/332
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/260, 21/330, 742/332 i.e 1/712140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/260, 21/330, 742/332.
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 34/260,21/330,742/332?
Given fractions are 34/260,21/330,742/332
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 34/260,21/330,742/332, numerators are 34,21,742
Denominators are 260,330,332
The GCF of 34,21,742 is 1 .
LCM of 260,330,332 is 712140.
The greatest common factor of 34/260,21/330,742/332 = [GCF of 34,21,742]/[LCM of 260,330,332]= 1/712140
Therefore, the GCF of 34/260,21/330,742/332 is 1/712140.
To find the highest common factor of 34,21,742, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 21 are 1, 3, 7, 21
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The HCF of 34,21,742 is 1.
Lets's calculate GCF of 34,21,742
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 34,21,742 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Greatest Common Factor
We found the factors 34,21,742 . The biggest common factor number is the GCF number.
So the greatest common factor 34,21,742 is 1.
Lets's calculate LCM of 260,330,332
| 2 | 260, 330, 332 |
| 2 | 130, 165, 166 |
| 5 | 65, 165, 83 |
| 13, 33, 83 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 13 x 33 x 83 = 712140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/712140
Therefore, the GCF of Fractions 34/260,21/330,742/332 is 1/712140
Least Common Multiple of 260,330,332 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 260,330,332 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(260,330,332) = 2
common factors(in case of two or more numbers have common factors) = 20
GCF(260,330,332) x common factors =2 x 20 = 40
LCM(260,330,332) = ( 260 × 330 × 332 ) / 40
LCM(260,330,332) = 28485600 / 40
LCM(260,330,332) = 712140
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FAQs on GCF of Fractions of 34/260, 21/330, 742/332
1. What is the HCF of 34,21,742?
The HCF of 34,21,742 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 34/260, 21/330, 742/332?
Answer: GCF of Numerators as per given numbers 34/260, 21/330, 742/332 is
GCF of Numerators i.e. for 34,21,742 is 1
LCM of denominators i.e. for 260,330,332 is 712140.
Thus, GCF of Fractions is 1/712140.Finally, GCF of Fractions for 34/260, 21/330, 742/332 is 1/712140.