GCF of 7105/946, 8214/4342
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7105/946, 8214/4342 i.e 1/2053766 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7105/946, 8214/4342.
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 7105/946,8214/4342?
Given fractions are 7105/946,8214/4342
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 7105/946,8214/4342, numerators are 7105,8214
Denominators are 946,4342
The GCF of 7105,8214 is 1 .
LCM of 946,4342 is 2053766.
The greatest common factor of 7105/946,8214/4342 = [GCF of 7105,8214]/[LCM of 946,4342]= 1/2053766
Therefore, the GCF of 7105/946,8214/4342 is 1/2053766.
To find the highest common factor of 7105,8214, we have to find the factors of both numbers and list the highest common factor.
The factors of 7105 are 1, 5, 7, 29, 35, 49, 145, 203, 245, 1015, 1421, 7105
The factors of 8214 are 1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214
The HCF of 7105,8214 is 1.
Lets's calculate GCF of 7105,8214
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7105,8214 By Matching Biggest Common Factor Method
Now, list down the factors of 7105
:1,5,7,29,35,49,145,203,245,1015,1421,7105
Now, list down the factors of 8214
:1,2,3,6,37,74,111,222,1369,2738,4107,8214
Greatest Common Factor
We found the factors 7105,8214 . The biggest common factor number is the GCF number.
So the greatest common factor 7105,8214 is 1.
Lets's calculate LCM of 946,4342
| 2 | 946, 4342 |
| 473, 2171 |
∴ So the LCM of the given numbers is 2 x 473 x 2171 = 2053766
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2053766
Therefore, the GCF of Fractions 7105/946,8214/4342 is 1/2053766
Least Common Multiple of 946,4342 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 946,4342 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(946,4342) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(946,4342) x common factors =2 x 1 = 2
LCM(946,4342) = ( 946 × 4342 ) / 2
LCM(946,4342) = 4107532 / 2
LCM(946,4342) = 2053766
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FAQs on GCF of Fractions of 7105/946, 8214/4342
1. What is the HCF of 7105,8214?
The HCF of 7105,8214 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 7105/946, 8214/4342?
Answer: GCF of Numerators as per given numbers 7105/946, 8214/4342 is
GCF of Numerators i.e. for 7105,8214 is 1
LCM of denominators i.e. for 946,4342 is 2053766.
Thus, GCF of Fractions is 1/2053766.Finally, GCF of Fractions for 7105/946, 8214/4342 is 1/2053766.