GCF of 772/133, 2254/749
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 772/133, 2254/749 i.e 2/14231 easily. The following is the detailed procedure to determine the greatest common factor of fractions 772/133, 2254/749.
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 772/133,2254/749?
Given fractions are 772/133,2254/749
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 772/133,2254/749, numerators are 772,2254
Denominators are 133,749
The GCF of 772,2254 is 2 .
LCM of 133,749 is 14231.
The greatest common factor of 772/133,2254/749 = [GCF of 772,2254]/[LCM of 133,749]= 2/14231
Therefore, the GCF of 772/133,2254/749 is 2/14231.
To find the highest common factor of 772,2254, we have to find the factors of both numbers and list the highest common factor.
The factors of 772 are 1, 2, 4, 193, 386, 772
The factors of 2254 are 1, 2, 7, 14, 23, 46, 49, 98, 161, 322, 1127, 2254
The HCF of 772,2254 is 2.
Lets's calculate GCF of 772,2254
| 2 | 772, 2254 |
| 386, 1127 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 772,2254 By Matching Biggest Common Factor Method
Now, list down the factors of 772
:1,2,4,193,386,772
Now, list down the factors of 2254
:1,2,7,14,23,46,49,98,161,322,1127,2254
Greatest Common Factor
We found the factors 772,2254 . The biggest common factor number is the GCF number.
So the greatest common factor 772,2254 is 2.
Lets's calculate LCM of 133,749
| 7 | 133, 749 |
| 19, 107 |
∴ So the LCM of the given numbers is 7 x 19 x 107 = 14231
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/14231
Therefore, the GCF of Fractions 772/133,2254/749 is 2/14231
Least Common Multiple of 133,749 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 133,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(133,749) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(133,749) x common factors =7 x 1 = 7
LCM(133,749) = ( 133 × 749 ) / 7
LCM(133,749) = 99617 / 7
LCM(133,749) = 14231
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FAQs on GCF of Fractions of 772/133, 2254/749
1. What is the HCF of 772,2254?
The HCF of 772,2254 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 772/133, 2254/749?
Answer: GCF of Numerators as per given numbers 772/133, 2254/749 is
GCF of Numerators i.e. for 772,2254 is 2
LCM of denominators i.e. for 133,749 is 14231.
Thus, GCF of Fractions is 2/14231.Finally, GCF of Fractions for 772/133, 2254/749 is 2/14231.