GCF of 78/137, 83/182, 180/169
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 78/137, 83/182, 180/169 i.e 1/324142 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/137, 83/182, 180/169.
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 78/137,83/182,180/169?
Given fractions are 78/137,83/182,180/169
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 78/137,83/182,180/169, numerators are 78,83,180
Denominators are 137,182,169
The GCF of 78,83,180 is 1 .
LCM of 137,182,169 is 324142.
The greatest common factor of 78/137,83/182,180/169 = [GCF of 78,83,180]/[LCM of 137,182,169]= 1/324142
Therefore, the GCF of 78/137,83/182,180/169 is 1/324142.
To find the highest common factor of 78,83,180, we have to find the factors of both numbers and list the highest common factor.
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 83 are 1, 83
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The HCF of 78,83,180 is 1.
Lets's calculate GCF of 78,83,180
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 78,83,180 By Matching Biggest Common Factor Method
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 83
:1,83
Now, list down the factors of 180
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
Greatest Common Factor
We found the factors 78,83,180 . The biggest common factor number is the GCF number.
So the greatest common factor 78,83,180 is 1.
Lets's calculate LCM of 137,182,169
| 13 | 137, 182, 169 |
| 137, 14, 13 |
∴ So the LCM of the given numbers is 13 x 137 x 14 x 13 = 324142
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/324142
Therefore, the GCF of Fractions 78/137,83/182,180/169 is 1/324142
Least Common Multiple of 137,182,169 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 137,182,169 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(137,182,169) = 1
common factors(in case of two or more numbers have common factors) = 13
GCF(137,182,169) x common factors =1 x 13 = 13
LCM(137,182,169) = ( 137 × 182 × 169 ) / 13
LCM(137,182,169) = 4213846 / 13
LCM(137,182,169) = 324142
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FAQs on GCF of Fractions of 78/137, 83/182, 180/169
1. What is the HCF of 78,83,180?
The HCF of 78,83,180 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 78/137, 83/182, 180/169?
Answer: GCF of Numerators as per given numbers 78/137, 83/182, 180/169 is
GCF of Numerators i.e. for 78,83,180 is 1
LCM of denominators i.e. for 137,182,169 is 324142.
Thus, GCF of Fractions is 1/324142.Finally, GCF of Fractions for 78/137, 83/182, 180/169 is 1/324142.