GCF of 54/288, 78/682, 160/639
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 54/288, 78/682, 160/639 i.e 2/6972768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/288, 78/682, 160/639.
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 54/288,78/682,160/639?
Given fractions are 54/288,78/682,160/639
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 54/288,78/682,160/639, numerators are 54,78,160
Denominators are 288,682,639
The GCF of 54,78,160 is 2 .
LCM of 288,682,639 is 6972768.
The greatest common factor of 54/288,78/682,160/639 = [GCF of 54,78,160]/[LCM of 288,682,639]= 2/6972768
Therefore, the GCF of 54/288,78/682,160/639 is 2/6972768.
To find the highest common factor of 54,78,160, we have to find the factors of both numbers and list the highest common factor.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The HCF of 54,78,160 is 2.
Lets's calculate GCF of 54,78,160
| 2 | 54, 78, 160 |
| 27, 39, 80 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 54,78,160 By Matching Biggest Common Factor Method
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Greatest Common Factor
We found the factors 54,78,160 . The biggest common factor number is the GCF number.
So the greatest common factor 54,78,160 is 2.
Lets's calculate LCM of 288,682,639
| 2 | 288, 682, 639 |
| 3 | 144, 341, 639 |
| 3 | 48, 341, 213 |
| 16, 341, 71 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 16 x 341 x 71 = 6972768
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6972768
Therefore, the GCF of Fractions 54/288,78/682,160/639 is 2/6972768
Least Common Multiple of 288,682,639 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 288,682,639 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(288,682,639) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(288,682,639) x common factors =1 x 18 = 18
LCM(288,682,639) = ( 288 × 682 × 639 ) / 18
LCM(288,682,639) = 125509824 / 18
LCM(288,682,639) = 6972768
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FAQs on GCF of Fractions of 54/288, 78/682, 160/639
1. What is the HCF of 54,78,160?
The HCF of 54,78,160 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 54/288, 78/682, 160/639?
Answer: GCF of Numerators as per given numbers 54/288, 78/682, 160/639 is
GCF of Numerators i.e. for 54,78,160 is 2
LCM of denominators i.e. for 288,682,639 is 6972768.
Thus, GCF of Fractions is 2/6972768.Finally, GCF of Fractions for 54/288, 78/682, 160/639 is 2/6972768.