Use our free GCF of Fractions Calculator tool to compute the GCF of 46/63, 128/84, 474/167 i.e 2/42084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/63, 128/84, 474/167.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 46/63,128/84,474/167
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 46/63,128/84,474/167, numerators are 46,128,474
Denominators are 63,84,167
The GCF of 46,128,474 is 2 .
LCM of 63,84,167 is 42084.
The greatest common factor of 46/63,128/84,474/167 = [GCF of 46,128,474]/[LCM of 63,84,167]= 2/42084
Therefore, the GCF of 46/63,128/84,474/167 is 2/42084.
To find the highest common factor of 46,128,474, we have to find the factors of both numbers and list the highest common factor.
The factors of 46 are 1, 2, 23, 46
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
The factors of 474 are 1, 2, 3, 6, 79, 158, 237, 474
The HCF of 46,128,474 is 2.
Lets's calculate GCF of 46,128,474
2 | 46, 128, 474 |
23, 64, 237 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 46
:1,2,23,46
Now, list down the factors of 128
:1,2,4,8,16,32,64,128
Now, list down the factors of 474
:1,2,3,6,79,158,237,474
Greatest Common Factor
We found the factors 46,128,474 . The biggest common factor number is the GCF number.
So the greatest common factor 46,128,474 is 2.
Lets's calculate LCM of 63,84,167
3 | 63, 84, 167 |
7 | 21, 28, 167 |
3, 4, 167 |
∴ So the LCM of the given numbers is 3 x 7 x 3 x 4 x 167 = 42084
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/42084
Therefore, the GCF of Fractions 46/63,128/84,474/167 is 2/42084
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 63,84,167 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(63,84,167) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(63,84,167) x common factors =1 x 21 = 21
LCM(63,84,167) = ( 63 × 84 × 167 ) / 21
LCM(63,84,167) = 883764 / 21
LCM(63,84,167) = 42084
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 46,128,474?
The HCF of 46,128,474 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 46/63, 128/84, 474/167?
Answer: GCF of Numerators as per given numbers 46/63, 128/84, 474/167 is
GCF of Numerators i.e. for 46,128,474 is 2
LCM of denominators i.e. for 63,84,167 is 42084.
Thus, GCF of Fractions is 2/42084.Finally, GCF of Fractions for 46/63, 128/84, 474/167 is 2/42084.