GCF of 35/450, 422/770, 314/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 35/450, 422/770, 314/814 i.e 1/1282050 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/450, 422/770, 314/814.
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 35/450,422/770,314/814?
Given fractions are 35/450,422/770,314/814
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 35/450,422/770,314/814, numerators are 35,422,314
Denominators are 450,770,814
The GCF of 35,422,314 is 1 .
LCM of 450,770,814 is 1282050.
The greatest common factor of 35/450,422/770,314/814 = [GCF of 35,422,314]/[LCM of 450,770,814]= 1/1282050
Therefore, the GCF of 35/450,422/770,314/814 is 1/1282050.
To find the highest common factor of 35,422,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 35 are 1, 5, 7, 35
The factors of 422 are 1, 2, 211, 422
The factors of 314 are 1, 2, 157, 314
The HCF of 35,422,314 is 1.
Lets's calculate GCF of 35,422,314
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 35,422,314 By Matching Biggest Common Factor Method
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 422
:1,2,211,422
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 35,422,314 . The biggest common factor number is the GCF number.
So the greatest common factor 35,422,314 is 1.
Lets's calculate LCM of 450,770,814
| 2 | 450, 770, 814 |
| 5 | 225, 385, 407 |
| 11 | 45, 77, 407 |
| 45, 7, 37 |
∴ So the LCM of the given numbers is 2 x 5 x 11 x 45 x 7 x 37 = 1282050
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1282050
Therefore, the GCF of Fractions 35/450,422/770,314/814 is 1/1282050
Least Common Multiple of 450,770,814 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 450,770,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(450,770,814) = 2
common factors(in case of two or more numbers have common factors) = 110
GCF(450,770,814) x common factors =2 x 110 = 220
LCM(450,770,814) = ( 450 × 770 × 814 ) / 220
LCM(450,770,814) = 282051000 / 220
LCM(450,770,814) = 1282050
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FAQs on GCF of Fractions of 35/450, 422/770, 314/814
1. What is the HCF of 35,422,314?
The HCF of 35,422,314 is 1
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 35/450, 422/770, 314/814?
Answer: GCF of Numerators as per given numbers 35/450, 422/770, 314/814 is
GCF of Numerators i.e. for 35,422,314 is 1
LCM of denominators i.e. for 450,770,814 is 1282050.
Thus, GCF of Fractions is 1/1282050.Finally, GCF of Fractions for 35/450, 422/770, 314/814 is 1/1282050.