GCF of 3686/971, 6916/4151
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3686/971, 6916/4151 i.e 38/4030621 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3686/971, 6916/4151.
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 3686/971,6916/4151?
Given fractions are 3686/971,6916/4151
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 3686/971,6916/4151, numerators are 3686,6916
Denominators are 971,4151
The GCF of 3686,6916 is 38 .
LCM of 971,4151 is 4030621.
The greatest common factor of 3686/971,6916/4151 = [GCF of 3686,6916]/[LCM of 971,4151]= 38/4030621
Therefore, the GCF of 3686/971,6916/4151 is 38/4030621.
To find the highest common factor of 3686,6916, we have to find the factors of both numbers and list the highest common factor.
The factors of 3686 are 1, 2, 19, 38, 97, 194, 1843, 3686
The factors of 6916 are 1, 2, 4, 7, 13, 14, 19, 26, 28, 38, 52, 76, 91, 133, 182, 247, 266, 364, 494, 532, 988, 1729, 3458, 6916
The HCF of 3686,6916 is 38.
Lets's calculate GCF of 3686,6916
| 2 | 3686, 6916 |
| 19 | 1843, 3458 |
| 97, 182 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 3686,6916 By Matching Biggest Common Factor Method
Now, list down the factors of 3686
:1,2,19,38,97,194,1843,3686
Now, list down the factors of 6916
:1,2,4,7,13,14,19,26,28,38,52,76,91,133,182,247,266,364,494,532,988,1729,3458,6916
Greatest Common Factor
We found the factors 3686,6916 . The biggest common factor number is the GCF number.
So the greatest common factor 3686,6916 is 38.
Lets's calculate LCM of 971,4151
Given numbers has no common factors except 1. So, there LCM is their product i.e 4030621
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/4030621
Therefore, the GCF of Fractions 3686/971,6916/4151 is 38/4030621
Least Common Multiple of 971,4151 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 971,4151 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(971,4151) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(971,4151) x common factors =1 x 1 = 1
LCM(971,4151) = ( 971 × 4151 ) / 1
LCM(971,4151) = 4030621 / 1
LCM(971,4151) = 4030621
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 3686/971, 6916/4151
1. What is the HCF of 3686,6916?
The HCF of 3686,6916 is 38
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 3686/971, 6916/4151?
Answer: GCF of Numerators as per given numbers 3686/971, 6916/4151 is
GCF of Numerators i.e. for 3686,6916 is 38
LCM of denominators i.e. for 971,4151 is 4030621.
Thus, GCF of Fractions is 38/4030621.Finally, GCF of Fractions for 3686/971, 6916/4151 is 38/4030621.