GCF of 817/42, 974/2106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 817/42, 974/2106 i.e 1/14742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 817/42, 974/2106.
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 817/42,974/2106?
Given fractions are 817/42,974/2106
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 817/42,974/2106, numerators are 817,974
Denominators are 42,2106
The GCF of 817,974 is 1 .
LCM of 42,2106 is 14742.
The greatest common factor of 817/42,974/2106 = [GCF of 817,974]/[LCM of 42,2106]= 1/14742
Therefore, the GCF of 817/42,974/2106 is 1/14742.
To find the highest common factor of 817,974, we have to find the factors of both numbers and list the highest common factor.
The factors of 817 are 1, 19, 43, 817
The factors of 974 are 1, 2, 487, 974
The HCF of 817,974 is 1.
Lets's calculate GCF of 817,974
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 817,974 By Matching Biggest Common Factor Method
Now, list down the factors of 817
:1,19,43,817
Now, list down the factors of 974
:1,2,487,974
Greatest Common Factor
We found the factors 817,974 . The biggest common factor number is the GCF number.
So the greatest common factor 817,974 is 1.
Lets's calculate LCM of 42,2106
| 2 | 42, 2106 |
| 3 | 21, 1053 |
| 7, 351 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 351 = 14742
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14742
Therefore, the GCF of Fractions 817/42,974/2106 is 1/14742
Least Common Multiple of 42,2106 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 42,2106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,2106) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(42,2106) x common factors =6 x 1 = 6
LCM(42,2106) = ( 42 × 2106 ) / 6
LCM(42,2106) = 88452 / 6
LCM(42,2106) = 14742
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FAQs on GCF of Fractions of 817/42, 974/2106
1. What is the HCF of 817,974?
The HCF of 817,974 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 817/42, 974/2106?
Answer: GCF of Numerators as per given numbers 817/42, 974/2106 is
GCF of Numerators i.e. for 817,974 is 1
LCM of denominators i.e. for 42,2106 is 14742.
Thus, GCF of Fractions is 1/14742.Finally, GCF of Fractions for 817/42, 974/2106 is 1/14742.