GCF of 682/276, 6974/735
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 682/276, 6974/735 i.e 22/67620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 682/276, 6974/735.
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 682/276,6974/735?
Given fractions are 682/276,6974/735
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 682/276,6974/735, numerators are 682,6974
Denominators are 276,735
The GCF of 682,6974 is 22 .
LCM of 276,735 is 67620.
The greatest common factor of 682/276,6974/735 = [GCF of 682,6974]/[LCM of 276,735]= 22/67620
Therefore, the GCF of 682/276,6974/735 is 22/67620.
To find the highest common factor of 682,6974, we have to find the factors of both numbers and list the highest common factor.
The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682
The factors of 6974 are 1, 2, 11, 22, 317, 634, 3487, 6974
The HCF of 682,6974 is 22.
Lets's calculate GCF of 682,6974
| 2 | 682, 6974 |
| 11 | 341, 3487 |
| 31, 317 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 682,6974 By Matching Biggest Common Factor Method
Now, list down the factors of 682
:1,2,11,22,31,62,341,682
Now, list down the factors of 6974
:1,2,11,22,317,634,3487,6974
Greatest Common Factor
We found the factors 682,6974 . The biggest common factor number is the GCF number.
So the greatest common factor 682,6974 is 22.
Lets's calculate LCM of 276,735
| 3 | 276, 735 |
| 92, 245 |
∴ So the LCM of the given numbers is 3 x 92 x 245 = 67620
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/67620
Therefore, the GCF of Fractions 682/276,6974/735 is 22/67620
Least Common Multiple of 276,735 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 276,735 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(276,735) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(276,735) x common factors =3 x 1 = 3
LCM(276,735) = ( 276 × 735 ) / 3
LCM(276,735) = 202860 / 3
LCM(276,735) = 67620
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FAQs on GCF of Fractions of 682/276, 6974/735
1. What is the HCF of 682,6974?
The HCF of 682,6974 is 22
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 682/276, 6974/735?
Answer: GCF of Numerators as per given numbers 682/276, 6974/735 is
GCF of Numerators i.e. for 682,6974 is 22
LCM of denominators i.e. for 276,735 is 67620.
Thus, GCF of Fractions is 22/67620.Finally, GCF of Fractions for 682/276, 6974/735 is 22/67620.