GCF of 654/491, 704/431
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 654/491, 704/431 i.e 2/211621 easily. The following is the detailed procedure to determine the greatest common factor of fractions 654/491, 704/431.
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 654/491,704/431?
Given fractions are 654/491,704/431
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 654/491,704/431, numerators are 654,704
Denominators are 491,431
The GCF of 654,704 is 2 .
LCM of 491,431 is 211621.
The greatest common factor of 654/491,704/431 = [GCF of 654,704]/[LCM of 491,431]= 2/211621
Therefore, the GCF of 654/491,704/431 is 2/211621.
To find the highest common factor of 654,704, we have to find the factors of both numbers and list the highest common factor.
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704
The HCF of 654,704 is 2.
Lets's calculate GCF of 654,704
| 2 | 654, 704 |
| 327, 352 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 654,704 By Matching Biggest Common Factor Method
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Now, list down the factors of 704
:1,2,4,8,11,16,22,32,44,64,88,176,352,704
Greatest Common Factor
We found the factors 654,704 . The biggest common factor number is the GCF number.
So the greatest common factor 654,704 is 2.
Lets's calculate LCM of 491,431
Given numbers has no common factors except 1. So, there LCM is their product i.e 211621
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/211621
Therefore, the GCF of Fractions 654/491,704/431 is 2/211621
Least Common Multiple of 491,431 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 491,431 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(491,431) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(491,431) x common factors =1 x 1 = 1
LCM(491,431) = ( 491 × 431 ) / 1
LCM(491,431) = 211621 / 1
LCM(491,431) = 211621
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FAQs on GCF of Fractions of 654/491, 704/431
1. What is the HCF of 654,704?
The HCF of 654,704 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 654/491, 704/431?
Answer: GCF of Numerators as per given numbers 654/491, 704/431 is
GCF of Numerators i.e. for 654,704 is 2
LCM of denominators i.e. for 491,431 is 211621.
Thus, GCF of Fractions is 2/211621.Finally, GCF of Fractions for 654/491, 704/431 is 2/211621.