Use our free GCF of Fractions Calculator tool to compute the GCF of 476/354, 972/422 i.e 4/74694 easily. The following is the detailed procedure to determine the greatest common factor of fractions 476/354, 972/422.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 476/354,972/422
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 476/354,972/422, numerators are 476,972
Denominators are 354,422
The GCF of 476,972 is 4 .
LCM of 354,422 is 74694.
The greatest common factor of 476/354,972/422 = [GCF of 476,972]/[LCM of 354,422]= 4/74694
Therefore, the GCF of 476/354,972/422 is 4/74694.
To find the highest common factor of 476,972, we have to find the factors of both numbers and list the highest common factor.
The factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The HCF of 476,972 is 4.
Lets's calculate GCF of 476,972
2 | 476, 972 |
2 | 238, 486 |
119, 243 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 476
:1,2,4,7,14,17,28,34,68,119,238,476
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Greatest Common Factor
We found the factors 476,972 . The biggest common factor number is the GCF number.
So the greatest common factor 476,972 is 4.
Lets's calculate LCM of 354,422
2 | 354, 422 |
177, 211 |
∴ So the LCM of the given numbers is 2 x 177 x 211 = 74694
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/74694
Therefore, the GCF of Fractions 476/354,972/422 is 4/74694
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 354,422 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(354,422) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(354,422) x common factors =2 x 1 = 2
LCM(354,422) = ( 354 × 422 ) / 2
LCM(354,422) = 149388 / 2
LCM(354,422) = 74694
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 476,972?
The HCF of 476,972 is 4
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 476/354, 972/422?
Answer: GCF of Numerators as per given numbers 476/354, 972/422 is
GCF of Numerators i.e. for 476,972 is 4
LCM of denominators i.e. for 354,422 is 74694.
Thus, GCF of Fractions is 4/74694.Finally, GCF of Fractions for 476/354, 972/422 is 4/74694.