GCF of 899/82, 682/709
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 899/82, 682/709 i.e 31/58138 easily. The following is the detailed procedure to determine the greatest common factor of fractions 899/82, 682/709.
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 899/82,682/709?
Given fractions are 899/82,682/709
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 899/82,682/709, numerators are 899,682
Denominators are 82,709
The GCF of 899,682 is 31 .
LCM of 82,709 is 58138.
The greatest common factor of 899/82,682/709 = [GCF of 899,682]/[LCM of 82,709]= 31/58138
Therefore, the GCF of 899/82,682/709 is 31/58138.
To find the highest common factor of 899,682, we have to find the factors of both numbers and list the highest common factor.
The factors of 899 are 1, 29, 31, 899
The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682
The HCF of 899,682 is 31.
Lets's calculate GCF of 899,682
| 31 | 899, 682 |
| 29, 22 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 899,682 By Matching Biggest Common Factor Method
Now, list down the factors of 899
:1,29,31,899
Now, list down the factors of 682
:1,2,11,22,31,62,341,682
Greatest Common Factor
We found the factors 899,682 . The biggest common factor number is the GCF number.
So the greatest common factor 899,682 is 31.
Lets's calculate LCM of 82,709
Given numbers has no common factors except 1. So, there LCM is their product i.e 58138
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/58138
Therefore, the GCF of Fractions 899/82,682/709 is 31/58138
Least Common Multiple of 82,709 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 82,709 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,709) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(82,709) x common factors =1 x 1 = 1
LCM(82,709) = ( 82 × 709 ) / 1
LCM(82,709) = 58138 / 1
LCM(82,709) = 58138
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FAQs on GCF of Fractions of 899/82, 682/709
1. What is the HCF of 899,682?
The HCF of 899,682 is 31
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 899/82, 682/709?
Answer: GCF of Numerators as per given numbers 899/82, 682/709 is
GCF of Numerators i.e. for 899,682 is 31
LCM of denominators i.e. for 82,709 is 58138.
Thus, GCF of Fractions is 31/58138.Finally, GCF of Fractions for 899/82, 682/709 is 31/58138.