GCF of 67/68, 14/60, 84/20, 42/86
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 67/68, 14/60, 84/20, 42/86 i.e 1/43860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 67/68, 14/60, 84/20, 42/86.
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 67/68,14/60,84/20,42/86?
Given fractions are 67/68,14/60,84/20,42/86
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 67/68,14/60,84/20,42/86, numerators are 67,14,84,42
Denominators are 68,60,20,86
The GCF of 67,14,84,42 is 1 .
LCM of 68,60,20,86 is 43860.
The greatest common factor of 67/68,14/60,84/20,42/86 = [GCF of 67,14,84,42]/[LCM of 68,60,20,86]= 1/43860
Therefore, the GCF of 67/68,14/60,84/20,42/86 is 1/43860.
To find the highest common factor of 67,14,84,42, we have to find the factors of both numbers and list the highest common factor.
The factors of 67 are 1, 67
The factors of 14 are 1, 2, 7, 14
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The HCF of 67,14,84,42 is 1.
Lets's calculate GCF of 67,14,84,42
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 67,14,84,42 By Matching Biggest Common Factor Method
Now, list down the factors of 67
:1,67
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Greatest Common Factor
We found the factors 67,14,84,42 . The biggest common factor number is the GCF number.
So the greatest common factor 67,14,84,42 is 1.
Lets's calculate LCM of 68,60,20,86
| 2 | 68, 60, 20, 86 |
| 2 | 34, 30, 10, 43 |
| 5 | 17, 15, 5, 43 |
| 17, 3, 1, 43 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 17 x 3 x 1 x 43 = 43860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/43860
Therefore, the GCF of Fractions 67/68,14/60,84/20,42/86 is 1/43860
Least Common Multiple of 68,60,20,86 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 68,60,20,86 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,60,20,86) = 2
common factors(in case of two or more numbers have common factors) = 80
GCF(68,60,20,86) x common factors =2 x 80 = 160
LCM(68,60,20,86) = ( 68 × 60 × 20 × 86 ) / 160
LCM(68,60,20,86) = 7017600 / 160
LCM(68,60,20,86) = 43860
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 67/68, 14/60, 84/20, 42/86
1. What is the HCF of 67,14,84,42?
The HCF of 67,14,84,42 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 67/68, 14/60, 84/20, 42/86?
Answer: GCF of Numerators as per given numbers 67/68, 14/60, 84/20, 42/86 is
GCF of Numerators i.e. for 67,14,84,42 is 1
LCM of denominators i.e. for 68,60,20,86 is 43860.
Thus, GCF of Fractions is 1/43860.Finally, GCF of Fractions for 67/68, 14/60, 84/20, 42/86 is 1/43860.