GCF of 3782/414, 8729/7005
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3782/414, 8729/7005 i.e 1/966690 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3782/414, 8729/7005.
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 3782/414,8729/7005?
Given fractions are 3782/414,8729/7005
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 3782/414,8729/7005, numerators are 3782,8729
Denominators are 414,7005
The GCF of 3782,8729 is 1 .
LCM of 414,7005 is 966690.
The greatest common factor of 3782/414,8729/7005 = [GCF of 3782,8729]/[LCM of 414,7005]= 1/966690
Therefore, the GCF of 3782/414,8729/7005 is 1/966690.
To find the highest common factor of 3782,8729, we have to find the factors of both numbers and list the highest common factor.
The factors of 3782 are 1, 2, 31, 61, 62, 122, 1891, 3782
The factors of 8729 are 1, 7, 29, 43, 203, 301, 1247, 8729
The HCF of 3782,8729 is 1.
Lets's calculate GCF of 3782,8729
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3782,8729 By Matching Biggest Common Factor Method
Now, list down the factors of 3782
:1,2,31,61,62,122,1891,3782
Now, list down the factors of 8729
:1,7,29,43,203,301,1247,8729
Greatest Common Factor
We found the factors 3782,8729 . The biggest common factor number is the GCF number.
So the greatest common factor 3782,8729 is 1.
Lets's calculate LCM of 414,7005
| 3 | 414, 7005 |
| 138, 2335 |
∴ So the LCM of the given numbers is 3 x 138 x 2335 = 966690
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/966690
Therefore, the GCF of Fractions 3782/414,8729/7005 is 1/966690
Least Common Multiple of 414,7005 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 414,7005 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,7005) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(414,7005) x common factors =3 x 1 = 3
LCM(414,7005) = ( 414 × 7005 ) / 3
LCM(414,7005) = 2900070 / 3
LCM(414,7005) = 966690
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FAQs on GCF of Fractions of 3782/414, 8729/7005
1. What is the HCF of 3782,8729?
The HCF of 3782,8729 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 3782/414, 8729/7005?
Answer: GCF of Numerators as per given numbers 3782/414, 8729/7005 is
GCF of Numerators i.e. for 3782,8729 is 1
LCM of denominators i.e. for 414,7005 is 966690.
Thus, GCF of Fractions is 1/966690.Finally, GCF of Fractions for 3782/414, 8729/7005 is 1/966690.