GCF of 350/743, 280/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 350/743, 280/814 i.e 70/604802 easily. The following is the detailed procedure to determine the greatest common factor of fractions 350/743, 280/814.
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 350/743,280/814?
Given fractions are 350/743,280/814
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 350/743,280/814, numerators are 350,280
Denominators are 743,814
The GCF of 350,280 is 70 .
LCM of 743,814 is 604802.
The greatest common factor of 350/743,280/814 = [GCF of 350,280]/[LCM of 743,814]= 70/604802
Therefore, the GCF of 350/743,280/814 is 70/604802.
To find the highest common factor of 350,280, we have to find the factors of both numbers and list the highest common factor.
The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The HCF of 350,280 is 70.
Lets's calculate GCF of 350,280
| 2 | 350, 280 |
| 5 | 175, 140 |
| 7 | 35, 28 |
| 5, 4 |
∴ So the GCF of the given numbers is 2 x 5 x 7 = 70
Greatest Common Factor of 350,280 By Matching Biggest Common Factor Method
Now, list down the factors of 350
:1,2,5,7,10,14,25,35,50,70,175,350
Now, list down the factors of 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Greatest Common Factor
We found the factors 350,280 . The biggest common factor number is the GCF number.
So the greatest common factor 350,280 is 70.
Lets's calculate LCM of 743,814
Given numbers has no common factors except 1. So, there LCM is their product i.e 604802
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 70/604802
Therefore, the GCF of Fractions 350/743,280/814 is 70/604802
Least Common Multiple of 743,814 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 743,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(743,814) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(743,814) x common factors =1 x 1 = 1
LCM(743,814) = ( 743 × 814 ) / 1
LCM(743,814) = 604802 / 1
LCM(743,814) = 604802
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FAQs on GCF of Fractions of 350/743, 280/814
1. What is the HCF of 350,280?
The HCF of 350,280 is 70
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 350/743, 280/814?
Answer: GCF of Numerators as per given numbers 350/743, 280/814 is
GCF of Numerators i.e. for 350,280 is 70
LCM of denominators i.e. for 743,814 is 604802.
Thus, GCF of Fractions is 70/604802.Finally, GCF of Fractions for 350/743, 280/814 is 70/604802.