GCF of 747/269, 782/398
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 747/269, 782/398 i.e 1/107062 easily. The following is the detailed procedure to determine the greatest common factor of fractions 747/269, 782/398.
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 747/269,782/398?
Given fractions are 747/269,782/398
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 747/269,782/398, numerators are 747,782
Denominators are 269,398
The GCF of 747,782 is 1 .
LCM of 269,398 is 107062.
The greatest common factor of 747/269,782/398 = [GCF of 747,782]/[LCM of 269,398]= 1/107062
Therefore, the GCF of 747/269,782/398 is 1/107062.
To find the highest common factor of 747,782, we have to find the factors of both numbers and list the highest common factor.
The factors of 747 are 1, 3, 9, 83, 249, 747
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 747,782 is 1.
Lets's calculate GCF of 747,782
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 747,782 By Matching Biggest Common Factor Method
Now, list down the factors of 747
:1,3,9,83,249,747
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 747,782 . The biggest common factor number is the GCF number.
So the greatest common factor 747,782 is 1.
Lets's calculate LCM of 269,398
Given numbers has no common factors except 1. So, there LCM is their product i.e 107062
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/107062
Therefore, the GCF of Fractions 747/269,782/398 is 1/107062
Least Common Multiple of 269,398 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 269,398 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(269,398) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(269,398) x common factors =1 x 1 = 1
LCM(269,398) = ( 269 × 398 ) / 1
LCM(269,398) = 107062 / 1
LCM(269,398) = 107062
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FAQs on GCF of Fractions of 747/269, 782/398
1. What is the HCF of 747,782?
The HCF of 747,782 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 747/269, 782/398?
Answer: GCF of Numerators as per given numbers 747/269, 782/398 is
GCF of Numerators i.e. for 747,782 is 1
LCM of denominators i.e. for 269,398 is 107062.
Thus, GCF of Fractions is 1/107062.Finally, GCF of Fractions for 747/269, 782/398 is 1/107062.