Use our free GCF of Fractions Calculator tool to compute the GCF of 168/841, 357/224 i.e 21/188384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 168/841, 357/224.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 168/841,357/224
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 168/841,357/224, numerators are 168,357
Denominators are 841,224
The GCF of 168,357 is 21 .
LCM of 841,224 is 188384.
The greatest common factor of 168/841,357/224 = [GCF of 168,357]/[LCM of 841,224]= 21/188384
Therefore, the GCF of 168/841,357/224 is 21/188384.
To find the highest common factor of 168,357, we have to find the factors of both numbers and list the highest common factor.
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357
The HCF of 168,357 is 21.
Lets's calculate GCF of 168,357
3 | 168, 357 |
7 | 56, 119 |
8, 17 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Now, list down the factors of 168
:1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Now, list down the factors of 357
:1,3,7,17,21,51,119,357
Greatest Common Factor
We found the factors 168,357 . The biggest common factor number is the GCF number.
So the greatest common factor 168,357 is 21.
Lets's calculate LCM of 841,224
Given numbers has no common factors except 1. So, there LCM is their product i.e 188384
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/188384
Therefore, the GCF of Fractions 168/841,357/224 is 21/188384
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 841,224 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(841,224) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(841,224) x common factors =1 x 1 = 1
LCM(841,224) = ( 841 × 224 ) / 1
LCM(841,224) = 188384 / 1
LCM(841,224) = 188384
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 168,357?
The HCF of 168,357 is 21
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 168/841, 357/224?
Answer: GCF of Numerators as per given numbers 168/841, 357/224 is
GCF of Numerators i.e. for 168,357 is 21
LCM of denominators i.e. for 841,224 is 188384.
Thus, GCF of Fractions is 21/188384.Finally, GCF of Fractions for 168/841, 357/224 is 21/188384.