GCF of 277/343, 456/674
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 277/343, 456/674 i.e 1/231182 easily. The following is the detailed procedure to determine the greatest common factor of fractions 277/343, 456/674.
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 277/343,456/674?
Given fractions are 277/343,456/674
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 277/343,456/674, numerators are 277,456
Denominators are 343,674
The GCF of 277,456 is 1 .
LCM of 343,674 is 231182.
The greatest common factor of 277/343,456/674 = [GCF of 277,456]/[LCM of 343,674]= 1/231182
Therefore, the GCF of 277/343,456/674 is 1/231182.
To find the highest common factor of 277,456, we have to find the factors of both numbers and list the highest common factor.
The factors of 277 are 1, 277
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The HCF of 277,456 is 1.
Lets's calculate GCF of 277,456
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 277,456 By Matching Biggest Common Factor Method
Now, list down the factors of 277
:1,277
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 277,456 . The biggest common factor number is the GCF number.
So the greatest common factor 277,456 is 1.
Lets's calculate LCM of 343,674
Given numbers has no common factors except 1. So, there LCM is their product i.e 231182
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/231182
Therefore, the GCF of Fractions 277/343,456/674 is 1/231182
Least Common Multiple of 343,674 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 343,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(343,674) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(343,674) x common factors =1 x 1 = 1
LCM(343,674) = ( 343 × 674 ) / 1
LCM(343,674) = 231182 / 1
LCM(343,674) = 231182
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FAQs on GCF of Fractions of 277/343, 456/674
1. What is the HCF of 277,456?
The HCF of 277,456 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 277/343, 456/674?
Answer: GCF of Numerators as per given numbers 277/343, 456/674 is
GCF of Numerators i.e. for 277,456 is 1
LCM of denominators i.e. for 343,674 is 231182.
Thus, GCF of Fractions is 1/231182.Finally, GCF of Fractions for 277/343, 456/674 is 1/231182.