GCF of 60/18, 67/52, 138/84
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 60/18, 67/52, 138/84 i.e 1/3276 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/18, 67/52, 138/84.
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 60/18,67/52,138/84?
Given fractions are 60/18,67/52,138/84
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 60/18,67/52,138/84, numerators are 60,67,138
Denominators are 18,52,84
The GCF of 60,67,138 is 1 .
LCM of 18,52,84 is 3276.
The greatest common factor of 60/18,67/52,138/84 = [GCF of 60,67,138]/[LCM of 18,52,84]= 1/3276
Therefore, the GCF of 60/18,67/52,138/84 is 1/3276.
To find the highest common factor of 60,67,138, we have to find the factors of both numbers and list the highest common factor.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 67 are 1, 67
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The HCF of 60,67,138 is 1.
Lets's calculate GCF of 60,67,138
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 60,67,138 By Matching Biggest Common Factor Method
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 67
:1,67
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 60,67,138 . The biggest common factor number is the GCF number.
So the greatest common factor 60,67,138 is 1.
Lets's calculate LCM of 18,52,84
| 2 | 18, 52, 84 |
| 2 | 9, 26, 42 |
| 3 | 9, 13, 21 |
| 3, 13, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 13 x 7 = 3276
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3276
Therefore, the GCF of Fractions 60/18,67/52,138/84 is 1/3276
Least Common Multiple of 18,52,84 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 18,52,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(18,52,84) = 2
common factors(in case of two or more numbers have common factors) = 12
GCF(18,52,84) x common factors =2 x 12 = 24
LCM(18,52,84) = ( 18 × 52 × 84 ) / 24
LCM(18,52,84) = 78624 / 24
LCM(18,52,84) = 3276
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FAQs on GCF of Fractions of 60/18, 67/52, 138/84
1. What is the HCF of 60,67,138?
The HCF of 60,67,138 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 60/18, 67/52, 138/84?
Answer: GCF of Numerators as per given numbers 60/18, 67/52, 138/84 is
GCF of Numerators i.e. for 60,67,138 is 1
LCM of denominators i.e. for 18,52,84 is 3276.
Thus, GCF of Fractions is 1/3276.Finally, GCF of Fractions for 60/18, 67/52, 138/84 is 1/3276.