Use our free GCF of Fractions Calculator tool to compute the GCF of 67/64, 128/43, 429/428 i.e 1/294464 easily. The following is the detailed procedure to determine the greatest common factor of fractions 67/64, 128/43, 429/428.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 67/64,128/43,429/428
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 67/64,128/43,429/428, numerators are 67,128,429
Denominators are 64,43,428
The GCF of 67,128,429 is 1 .
LCM of 64,43,428 is 294464.
The greatest common factor of 67/64,128/43,429/428 = [GCF of 67,128,429]/[LCM of 64,43,428]= 1/294464
Therefore, the GCF of 67/64,128/43,429/428 is 1/294464.
To find the highest common factor of 67,128,429, we have to find the factors of both numbers and list the highest common factor.
The factors of 67 are 1, 67
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429
The HCF of 67,128,429 is 1.
Lets's calculate GCF of 67,128,429
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 67
:1,67
Now, list down the factors of 128
:1,2,4,8,16,32,64,128
Now, list down the factors of 429
:1,3,11,13,33,39,143,429
Greatest Common Factor
We found the factors 67,128,429 . The biggest common factor number is the GCF number.
So the greatest common factor 67,128,429 is 1.
Lets's calculate LCM of 64,43,428
2 | 64, 43, 428 |
2 | 32, 43, 214 |
16, 43, 107 |
∴ So the LCM of the given numbers is 2 x 2 x 16 x 43 x 107 = 294464
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/294464
Therefore, the GCF of Fractions 67/64,128/43,429/428 is 1/294464
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 64,43,428 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,43,428) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(64,43,428) x common factors =1 x 4 = 4
LCM(64,43,428) = ( 64 × 43 × 428 ) / 4
LCM(64,43,428) = 1177856 / 4
LCM(64,43,428) = 294464
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 67,128,429?
The HCF of 67,128,429 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 67/64, 128/43, 429/428?
Answer: GCF of Numerators as per given numbers 67/64, 128/43, 429/428 is
GCF of Numerators i.e. for 67,128,429 is 1
LCM of denominators i.e. for 64,43,428 is 294464.
Thus, GCF of Fractions is 1/294464.Finally, GCF of Fractions for 67/64, 128/43, 429/428 is 1/294464.