GCF of 974/38, 782/204
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 974/38, 782/204 i.e 2/3876 easily. The following is the detailed procedure to determine the greatest common factor of fractions 974/38, 782/204.
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 974/38,782/204?
Given fractions are 974/38,782/204
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 974/38,782/204, numerators are 974,782
Denominators are 38,204
The GCF of 974,782 is 2 .
LCM of 38,204 is 3876.
The greatest common factor of 974/38,782/204 = [GCF of 974,782]/[LCM of 38,204]= 2/3876
Therefore, the GCF of 974/38,782/204 is 2/3876.
To find the highest common factor of 974,782, we have to find the factors of both numbers and list the highest common factor.
The factors of 974 are 1, 2, 487, 974
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 974,782 is 2.
Lets's calculate GCF of 974,782
| 2 | 974, 782 |
| 487, 391 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 974,782 By Matching Biggest Common Factor Method
Now, list down the factors of 974
:1,2,487,974
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 974,782 . The biggest common factor number is the GCF number.
So the greatest common factor 974,782 is 2.
Lets's calculate LCM of 38,204
| 2 | 38, 204 |
| 19, 102 |
∴ So the LCM of the given numbers is 2 x 19 x 102 = 3876
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3876
Therefore, the GCF of Fractions 974/38,782/204 is 2/3876
Least Common Multiple of 38,204 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 38,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,204) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(38,204) x common factors =2 x 1 = 2
LCM(38,204) = ( 38 × 204 ) / 2
LCM(38,204) = 7752 / 2
LCM(38,204) = 3876
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FAQs on GCF of Fractions of 974/38, 782/204
1. What is the HCF of 974,782?
The HCF of 974,782 is 2
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 974/38, 782/204?
Answer: GCF of Numerators as per given numbers 974/38, 782/204 is
GCF of Numerators i.e. for 974,782 is 2
LCM of denominators i.e. for 38,204 is 3876.
Thus, GCF of Fractions is 2/3876.Finally, GCF of Fractions for 974/38, 782/204 is 2/3876.