GCF of 313/34, 782/278
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 313/34, 782/278 i.e 1/4726 easily. The following is the detailed procedure to determine the greatest common factor of fractions 313/34, 782/278.
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 313/34,782/278?
Given fractions are 313/34,782/278
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 313/34,782/278, numerators are 313,782
Denominators are 34,278
The GCF of 313,782 is 1 .
LCM of 34,278 is 4726.
The greatest common factor of 313/34,782/278 = [GCF of 313,782]/[LCM of 34,278]= 1/4726
Therefore, the GCF of 313/34,782/278 is 1/4726.
To find the highest common factor of 313,782, we have to find the factors of both numbers and list the highest common factor.
The factors of 313 are 1, 313
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 313,782 is 1.
Lets's calculate GCF of 313,782
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 313,782 By Matching Biggest Common Factor Method
Now, list down the factors of 313
:1,313
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 313,782 . The biggest common factor number is the GCF number.
So the greatest common factor 313,782 is 1.
Lets's calculate LCM of 34,278
| 2 | 34, 278 |
| 17, 139 |
∴ So the LCM of the given numbers is 2 x 17 x 139 = 4726
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4726
Therefore, the GCF of Fractions 313/34,782/278 is 1/4726
Least Common Multiple of 34,278 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 34,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,278) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,278) x common factors =2 x 1 = 2
LCM(34,278) = ( 34 × 278 ) / 2
LCM(34,278) = 9452 / 2
LCM(34,278) = 4726
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FAQs on GCF of Fractions of 313/34, 782/278
1. What is the HCF of 313,782?
The HCF of 313,782 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 313/34, 782/278?
Answer: GCF of Numerators as per given numbers 313/34, 782/278 is
GCF of Numerators i.e. for 313,782 is 1
LCM of denominators i.e. for 34,278 is 4726.
Thus, GCF of Fractions is 1/4726.Finally, GCF of Fractions for 313/34, 782/278 is 1/4726.