GCF of 904/80, 678/35, 680/20
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 904/80, 678/35, 680/20 i.e 2/560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 904/80, 678/35, 680/20.
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 904/80,678/35,680/20?
Given fractions are 904/80,678/35,680/20
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 904/80,678/35,680/20, numerators are 904,678,680
Denominators are 80,35,20
The GCF of 904,678,680 is 2 .
LCM of 80,35,20 is 560.
The greatest common factor of 904/80,678/35,680/20 = [GCF of 904,678,680]/[LCM of 80,35,20]= 2/560
Therefore, the GCF of 904/80,678/35,680/20 is 2/560.
To find the highest common factor of 904,678,680, we have to find the factors of both numbers and list the highest common factor.
The factors of 904 are 1, 2, 4, 8, 113, 226, 452, 904
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The HCF of 904,678,680 is 2.
Lets's calculate GCF of 904,678,680
| 2 | 904, 678, 680 |
| 452, 339, 340 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 904,678,680 By Matching Biggest Common Factor Method
Now, list down the factors of 904
:1,2,4,8,113,226,452,904
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Greatest Common Factor
We found the factors 904,678,680 . The biggest common factor number is the GCF number.
So the greatest common factor 904,678,680 is 2.
Lets's calculate LCM of 80,35,20
| 2 | 80, 35, 20 |
| 2 | 40, 35, 10 |
| 5 | 20, 35, 5 |
| 4, 7, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 4 x 7 x 1 = 560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/560
Therefore, the GCF of Fractions 904/80,678/35,680/20 is 2/560
Least Common Multiple of 80,35,20 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 80,35,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(80,35,20) = 5
common factors(in case of two or more numbers have common factors) = 20
GCF(80,35,20) x common factors =5 x 20 = 100
LCM(80,35,20) = ( 80 × 35 × 20 ) / 100
LCM(80,35,20) = 56000 / 100
LCM(80,35,20) = 560
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FAQs on GCF of Fractions of 904/80, 678/35, 680/20
1. What is the HCF of 904,678,680?
The HCF of 904,678,680 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 904/80, 678/35, 680/20?
Answer: GCF of Numerators as per given numbers 904/80, 678/35, 680/20 is
GCF of Numerators i.e. for 904,678,680 is 2
LCM of denominators i.e. for 80,35,20 is 560.
Thus, GCF of Fractions is 2/560.Finally, GCF of Fractions for 904/80, 678/35, 680/20 is 2/560.