GCF of 20/720, 78/136, 107/135
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 20/720, 78/136, 107/135 i.e 1/36720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/720, 78/136, 107/135.
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 20/720,78/136,107/135?
Given fractions are 20/720,78/136,107/135
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 20/720,78/136,107/135, numerators are 20,78,107
Denominators are 720,136,135
The GCF of 20,78,107 is 1 .
LCM of 720,136,135 is 36720.
The greatest common factor of 20/720,78/136,107/135 = [GCF of 20,78,107]/[LCM of 720,136,135]= 1/36720
Therefore, the GCF of 20/720,78/136,107/135 is 1/36720.
To find the highest common factor of 20,78,107, we have to find the factors of both numbers and list the highest common factor.
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 107 are 1, 107
The HCF of 20,78,107 is 1.
Lets's calculate GCF of 20,78,107
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 20,78,107 By Matching Biggest Common Factor Method
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 107
:1,107
Greatest Common Factor
We found the factors 20,78,107 . The biggest common factor number is the GCF number.
So the greatest common factor 20,78,107 is 1.
Lets's calculate LCM of 720,136,135
| 2 | 720, 136, 135 |
| 2 | 360, 68, 135 |
| 2 | 180, 34, 135 |
| 3 | 90, 17, 135 |
| 3 | 30, 17, 45 |
| 5 | 10, 17, 15 |
| 2, 17, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 5 x 2 x 17 x 3 = 36720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/36720
Therefore, the GCF of Fractions 20/720,78/136,107/135 is 1/36720
Least Common Multiple of 720,136,135 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 720,136,135 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(720,136,135) = 1
common factors(in case of two or more numbers have common factors) = 360
GCF(720,136,135) x common factors =1 x 360 = 360
LCM(720,136,135) = ( 720 × 136 × 135 ) / 360
LCM(720,136,135) = 13219200 / 360
LCM(720,136,135) = 36720
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FAQs on GCF of Fractions of 20/720, 78/136, 107/135
1. What is the HCF of 20,78,107?
The HCF of 20,78,107 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 20/720, 78/136, 107/135?
Answer: GCF of Numerators as per given numbers 20/720, 78/136, 107/135 is
GCF of Numerators i.e. for 20,78,107 is 1
LCM of denominators i.e. for 720,136,135 is 36720.
Thus, GCF of Fractions is 1/36720.Finally, GCF of Fractions for 20/720, 78/136, 107/135 is 1/36720.