GCF of 1954/429, 1469/286
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1954/429, 1469/286 i.e 1/858 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1954/429, 1469/286.
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 1954/429,1469/286?
Given fractions are 1954/429,1469/286
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 1954/429,1469/286, numerators are 1954,1469
Denominators are 429,286
The GCF of 1954,1469 is 1 .
LCM of 429,286 is 858.
The greatest common factor of 1954/429,1469/286 = [GCF of 1954,1469]/[LCM of 429,286]= 1/858
Therefore, the GCF of 1954/429,1469/286 is 1/858.
To find the highest common factor of 1954,1469, we have to find the factors of both numbers and list the highest common factor.
The factors of 1954 are 1, 2, 977, 1954
The factors of 1469 are 1, 13, 113, 1469
The HCF of 1954,1469 is 1.
Lets's calculate GCF of 1954,1469
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1954,1469 By Matching Biggest Common Factor Method
Now, list down the factors of 1954
:1,2,977,1954
Now, list down the factors of 1469
:1,13,113,1469
Greatest Common Factor
We found the factors 1954,1469 . The biggest common factor number is the GCF number.
So the greatest common factor 1954,1469 is 1.
Lets's calculate LCM of 429,286
| 11 | 429, 286 |
| 13 | 39, 26 |
| 3, 2 |
∴ So the LCM of the given numbers is 11 x 13 x 3 x 2 = 858
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/858
Therefore, the GCF of Fractions 1954/429,1469/286 is 1/858
Least Common Multiple of 429,286 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 429,286 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(429,286) = 143
common factors(in case of two or more numbers have common factors) = 1
GCF(429,286) x common factors =143 x 1 = 143
LCM(429,286) = ( 429 × 286 ) / 143
LCM(429,286) = 122694 / 143
LCM(429,286) = 858
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FAQs on GCF of Fractions of 1954/429, 1469/286
1. What is the HCF of 1954,1469?
The HCF of 1954,1469 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 1954/429, 1469/286?
Answer: GCF of Numerators as per given numbers 1954/429, 1469/286 is
GCF of Numerators i.e. for 1954,1469 is 1
LCM of denominators i.e. for 429,286 is 858.
Thus, GCF of Fractions is 1/858.Finally, GCF of Fractions for 1954/429, 1469/286 is 1/858.