GCF of 595/420, 830/280
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 595/420, 830/280 i.e 5/840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 595/420, 830/280.
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 595/420,830/280?
Given fractions are 595/420,830/280
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 595/420,830/280, numerators are 595,830
Denominators are 420,280
The GCF of 595,830 is 5 .
LCM of 420,280 is 840.
The greatest common factor of 595/420,830/280 = [GCF of 595,830]/[LCM of 420,280]= 5/840
Therefore, the GCF of 595/420,830/280 is 5/840.
To find the highest common factor of 595,830, we have to find the factors of both numbers and list the highest common factor.
The factors of 595 are 1, 5, 7, 17, 35, 85, 119, 595
The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830
The HCF of 595,830 is 5.
Lets's calculate GCF of 595,830
| 5 | 595, 830 |
| 119, 166 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 595,830 By Matching Biggest Common Factor Method
Now, list down the factors of 595
:1,5,7,17,35,85,119,595
Now, list down the factors of 830
:1,2,5,10,83,166,415,830
Greatest Common Factor
We found the factors 595,830 . The biggest common factor number is the GCF number.
So the greatest common factor 595,830 is 5.
Lets's calculate LCM of 420,280
| 2 | 420, 280 |
| 2 | 210, 140 |
| 5 | 105, 70 |
| 7 | 21, 14 |
| 3, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 7 x 3 x 2 = 840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/840
Therefore, the GCF of Fractions 595/420,830/280 is 5/840
Least Common Multiple of 420,280 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 420,280 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,280) = 140
common factors(in case of two or more numbers have common factors) = 1
GCF(420,280) x common factors =140 x 1 = 140
LCM(420,280) = ( 420 × 280 ) / 140
LCM(420,280) = 117600 / 140
LCM(420,280) = 840
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FAQs on GCF of Fractions of 595/420, 830/280
1. What is the HCF of 595,830?
The HCF of 595,830 is 5
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 595/420, 830/280?
Answer: GCF of Numerators as per given numbers 595/420, 830/280 is
GCF of Numerators i.e. for 595,830 is 5
LCM of denominators i.e. for 420,280 is 840.
Thus, GCF of Fractions is 5/840.Finally, GCF of Fractions for 595/420, 830/280 is 5/840.