GCF of 242/20, 774/9712
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 242/20, 774/9712 i.e 2/48560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 242/20, 774/9712.
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 242/20,774/9712?
Given fractions are 242/20,774/9712
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 242/20,774/9712, numerators are 242,774
Denominators are 20,9712
The GCF of 242,774 is 2 .
LCM of 20,9712 is 48560.
The greatest common factor of 242/20,774/9712 = [GCF of 242,774]/[LCM of 20,9712]= 2/48560
Therefore, the GCF of 242/20,774/9712 is 2/48560.
To find the highest common factor of 242,774, we have to find the factors of both numbers and list the highest common factor.
The factors of 242 are 1, 2, 11, 22, 121, 242
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The HCF of 242,774 is 2.
Lets's calculate GCF of 242,774
| 2 | 242, 774 |
| 121, 387 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 242,774 By Matching Biggest Common Factor Method
Now, list down the factors of 242
:1,2,11,22,121,242
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Greatest Common Factor
We found the factors 242,774 . The biggest common factor number is the GCF number.
So the greatest common factor 242,774 is 2.
Lets's calculate LCM of 20,9712
| 2 | 20, 9712 |
| 2 | 10, 4856 |
| 5, 2428 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 2428 = 48560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/48560
Therefore, the GCF of Fractions 242/20,774/9712 is 2/48560
Least Common Multiple of 20,9712 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 20,9712 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,9712) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(20,9712) x common factors =4 x 1 = 4
LCM(20,9712) = ( 20 × 9712 ) / 4
LCM(20,9712) = 194240 / 4
LCM(20,9712) = 48560
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FAQs on GCF of Fractions of 242/20, 774/9712
1. What is the HCF of 242,774?
The HCF of 242,774 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 242/20, 774/9712?
Answer: GCF of Numerators as per given numbers 242/20, 774/9712 is
GCF of Numerators i.e. for 242,774 is 2
LCM of denominators i.e. for 20,9712 is 48560.
Thus, GCF of Fractions is 2/48560.Finally, GCF of Fractions for 242/20, 774/9712 is 2/48560.