GCF of 221/54, 442/772
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 221/54, 442/772 i.e 221/20844 easily. The following is the detailed procedure to determine the greatest common factor of fractions 221/54, 442/772.
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 221/54,442/772?
Given fractions are 221/54,442/772
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 221/54,442/772, numerators are 221,442
Denominators are 54,772
The GCF of 221,442 is 221 .
LCM of 54,772 is 20844.
The greatest common factor of 221/54,442/772 = [GCF of 221,442]/[LCM of 54,772]= 221/20844
Therefore, the GCF of 221/54,442/772 is 221/20844.
To find the highest common factor of 221,442, we have to find the factors of both numbers and list the highest common factor.
The factors of 221 are 1, 13, 17, 221
The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442
The HCF of 221,442 is 221.
Lets's calculate GCF of 221,442
| 13 | 221, 442 |
| 17 | 17, 34 |
| 1, 2 |
∴ So the GCF of the given numbers is 13 x 17 = 221
Greatest Common Factor of 221,442 By Matching Biggest Common Factor Method
Now, list down the factors of 221
:1,13,17,221
Now, list down the factors of 442
:1,2,13,17,26,34,221,442
Greatest Common Factor
We found the factors 221,442 . The biggest common factor number is the GCF number.
So the greatest common factor 221,442 is 221.
Lets's calculate LCM of 54,772
| 2 | 54, 772 |
| 27, 386 |
∴ So the LCM of the given numbers is 2 x 27 x 386 = 20844
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 221/20844
Therefore, the GCF of Fractions 221/54,442/772 is 221/20844
Least Common Multiple of 54,772 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 54,772 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,772) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(54,772) x common factors =2 x 1 = 2
LCM(54,772) = ( 54 × 772 ) / 2
LCM(54,772) = 41688 / 2
LCM(54,772) = 20844
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FAQs on GCF of Fractions of 221/54, 442/772
1. What is the HCF of 221,442?
The HCF of 221,442 is 221
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 221/54, 442/772?
Answer: GCF of Numerators as per given numbers 221/54, 442/772 is
GCF of Numerators i.e. for 221,442 is 221
LCM of denominators i.e. for 54,772 is 20844.
Thus, GCF of Fractions is 221/20844.Finally, GCF of Fractions for 221/54, 442/772 is 221/20844.