GCF of 680/72, 460/400
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 680/72, 460/400 i.e 20/3600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 680/72, 460/400.
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 680/72,460/400?
Given fractions are 680/72,460/400
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 680/72,460/400, numerators are 680,460
Denominators are 72,400
The GCF of 680,460 is 20 .
LCM of 72,400 is 3600.
The greatest common factor of 680/72,460/400 = [GCF of 680,460]/[LCM of 72,400]= 20/3600
Therefore, the GCF of 680/72,460/400 is 20/3600.
To find the highest common factor of 680,460, we have to find the factors of both numbers and list the highest common factor.
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
The HCF of 680,460 is 20.
Lets's calculate GCF of 680,460
| 2 | 680, 460 |
| 2 | 340, 230 |
| 5 | 170, 115 |
| 34, 23 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 680,460 By Matching Biggest Common Factor Method
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Now, list down the factors of 460
:1,2,4,5,10,20,23,46,92,115,230,460
Greatest Common Factor
We found the factors 680,460 . The biggest common factor number is the GCF number.
So the greatest common factor 680,460 is 20.
Lets's calculate LCM of 72,400
| 2 | 72, 400 |
| 2 | 36, 200 |
| 2 | 18, 100 |
| 9, 50 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 9 x 50 = 3600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/3600
Therefore, the GCF of Fractions 680/72,460/400 is 20/3600
Least Common Multiple of 72,400 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 72,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,400) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(72,400) x common factors =8 x 1 = 8
LCM(72,400) = ( 72 × 400 ) / 8
LCM(72,400) = 28800 / 8
LCM(72,400) = 3600
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FAQs on GCF of Fractions of 680/72, 460/400
1. What is the HCF of 680,460?
The HCF of 680,460 is 20
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 680/72, 460/400?
Answer: GCF of Numerators as per given numbers 680/72, 460/400 is
GCF of Numerators i.e. for 680,460 is 20
LCM of denominators i.e. for 72,400 is 3600.
Thus, GCF of Fractions is 20/3600.Finally, GCF of Fractions for 680/72, 460/400 is 20/3600.