Use our free GCF of Fractions Calculator tool to compute the GCF of 178/421, 282/532 i.e 2/223972 easily. The following is the detailed procedure to determine the greatest common factor of fractions 178/421, 282/532.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 178/421,282/532
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 178/421,282/532, numerators are 178,282
Denominators are 421,532
The GCF of 178,282 is 2 .
LCM of 421,532 is 223972.
The greatest common factor of 178/421,282/532 = [GCF of 178,282]/[LCM of 421,532]= 2/223972
Therefore, the GCF of 178/421,282/532 is 2/223972.
To find the highest common factor of 178,282, we have to find the factors of both numbers and list the highest common factor.
The factors of 178 are 1, 2, 89, 178
The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282
The HCF of 178,282 is 2.
Lets's calculate GCF of 178,282
2 | 178, 282 |
89, 141 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 178
:1,2,89,178
Now, list down the factors of 282
:1,2,3,6,47,94,141,282
Greatest Common Factor
We found the factors 178,282 . The biggest common factor number is the GCF number.
So the greatest common factor 178,282 is 2.
Lets's calculate LCM of 421,532
Given numbers has no common factors except 1. So, there LCM is their product i.e 223972
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/223972
Therefore, the GCF of Fractions 178/421,282/532 is 2/223972
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 421,532 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(421,532) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(421,532) x common factors =1 x 1 = 1
LCM(421,532) = ( 421 × 532 ) / 1
LCM(421,532) = 223972 / 1
LCM(421,532) = 223972
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 178,282?
The HCF of 178,282 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 178/421, 282/532?
Answer: GCF of Numerators as per given numbers 178/421, 282/532 is
GCF of Numerators i.e. for 178,282 is 2
LCM of denominators i.e. for 421,532 is 223972.
Thus, GCF of Fractions is 2/223972.Finally, GCF of Fractions for 178/421, 282/532 is 2/223972.