GCF of 714/188, 8694/6586
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 714/188, 8694/6586 i.e 42/619084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 714/188, 8694/6586.
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 714/188,8694/6586?
Given fractions are 714/188,8694/6586
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 714/188,8694/6586, numerators are 714,8694
Denominators are 188,6586
The GCF of 714,8694 is 42 .
LCM of 188,6586 is 619084.
The greatest common factor of 714/188,8694/6586 = [GCF of 714,8694]/[LCM of 188,6586]= 42/619084
Therefore, the GCF of 714/188,8694/6586 is 42/619084.
To find the highest common factor of 714,8694, we have to find the factors of both numbers and list the highest common factor.
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The factors of 8694 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 23, 27, 42, 46, 54, 63, 69, 126, 138, 161, 189, 207, 322, 378, 414, 483, 621, 966, 1242, 1449, 2898, 4347, 8694
The HCF of 714,8694 is 42.
Lets's calculate GCF of 714,8694
| 2 | 714, 8694 |
| 3 | 357, 4347 |
| 7 | 119, 1449 |
| 17, 207 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
Greatest Common Factor of 714,8694 By Matching Biggest Common Factor Method
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Now, list down the factors of 8694
:1,2,3,6,7,9,14,18,21,23,27,42,46,54,63,69,126,138,161,189,207,322,378,414,483,621,966,1242,1449,2898,4347,8694
Greatest Common Factor
We found the factors 714,8694 . The biggest common factor number is the GCF number.
So the greatest common factor 714,8694 is 42.
Lets's calculate LCM of 188,6586
| 2 | 188, 6586 |
| 94, 3293 |
∴ So the LCM of the given numbers is 2 x 94 x 3293 = 619084
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/619084
Therefore, the GCF of Fractions 714/188,8694/6586 is 42/619084
Least Common Multiple of 188,6586 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 188,6586 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(188,6586) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(188,6586) x common factors =2 x 1 = 2
LCM(188,6586) = ( 188 × 6586 ) / 2
LCM(188,6586) = 1238168 / 2
LCM(188,6586) = 619084
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 714/188, 8694/6586
1. What is the HCF of 714,8694?
The HCF of 714,8694 is 42
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 714/188, 8694/6586?
Answer: GCF of Numerators as per given numbers 714/188, 8694/6586 is
GCF of Numerators i.e. for 714,8694 is 42
LCM of denominators i.e. for 188,6586 is 619084.
Thus, GCF of Fractions is 42/619084.Finally, GCF of Fractions for 714/188, 8694/6586 is 42/619084.