GCF of 14/45, 680/48, 670/200
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 14/45, 680/48, 670/200 i.e 2/3600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/45, 680/48, 670/200.
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 14/45,680/48,670/200?
Given fractions are 14/45,680/48,670/200
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 14/45,680/48,670/200, numerators are 14,680,670
Denominators are 45,48,200
The GCF of 14,680,670 is 2 .
LCM of 45,48,200 is 3600.
The greatest common factor of 14/45,680/48,670/200 = [GCF of 14,680,670]/[LCM of 45,48,200]= 2/3600
Therefore, the GCF of 14/45,680/48,670/200 is 2/3600.
To find the highest common factor of 14,680,670, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The factors of 670 are 1, 2, 5, 10, 67, 134, 335, 670
The HCF of 14,680,670 is 2.
Lets's calculate GCF of 14,680,670
| 2 | 14, 680, 670 |
| 7, 340, 335 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 14,680,670 By Matching Biggest Common Factor Method
Now, list down the factors of 14
:1,2,7,14
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 670
:1,2,5,10,67,134,335,670
Greatest Common Factor
We found the factors 14,680,670 . The biggest common factor number is the GCF number.
So the greatest common factor 14,680,670 is 2.
Lets's calculate LCM of 45,48,200
| 2 | 45, 48, 200 |
| 2 | 45, 24, 100 |
| 2 | 45, 12, 50 |
| 3 | 45, 6, 25 |
| 5 | 15, 2, 25 |
| 3, 2, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 3 x 2 x 5 = 3600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3600
Therefore, the GCF of Fractions 14/45,680/48,670/200 is 2/3600
Least Common Multiple of 45,48,200 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 45,48,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(45,48,200) = 1
common factors(in case of two or more numbers have common factors) = 120
GCF(45,48,200) x common factors =1 x 120 = 120
LCM(45,48,200) = ( 45 × 48 × 200 ) / 120
LCM(45,48,200) = 432000 / 120
LCM(45,48,200) = 3600
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FAQs on GCF of Fractions of 14/45, 680/48, 670/200
1. What is the HCF of 14,680,670?
The HCF of 14,680,670 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 14/45, 680/48, 670/200?
Answer: GCF of Numerators as per given numbers 14/45, 680/48, 670/200 is
GCF of Numerators i.e. for 14,680,670 is 2
LCM of denominators i.e. for 45,48,200 is 3600.
Thus, GCF of Fractions is 2/3600.Finally, GCF of Fractions for 14/45, 680/48, 670/200 is 2/3600.