GCF of 222/421, 105/611
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 222/421, 105/611 i.e 3/257231 easily. The following is the detailed procedure to determine the greatest common factor of fractions 222/421, 105/611.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 222/421,105/611?
Given fractions are 222/421,105/611
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 222/421,105/611, numerators are 222,105
Denominators are 421,611
The GCF of 222,105 is 3 .
LCM of 421,611 is 257231.
The greatest common factor of 222/421,105/611 = [GCF of 222,105]/[LCM of 421,611]= 3/257231
Therefore, the GCF of 222/421,105/611 is 3/257231.
To find the highest common factor of 222,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 222,105 is 3.
Lets's calculate GCF of 222,105
| 3 | 222, 105 |
| 74, 35 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 222,105 By Matching Biggest Common Factor Method
Now, list down the factors of 222
:1,2,3,6,37,74,111,222
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 222,105 . The biggest common factor number is the GCF number.
So the greatest common factor 222,105 is 3.
Lets's calculate LCM of 421,611
Given numbers has no common factors except 1. So, there LCM is their product i.e 257231
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/257231
Therefore, the GCF of Fractions 222/421,105/611 is 3/257231
Least Common Multiple of 421,611 with GCF Formula
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 421,611 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(421,611) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(421,611) x common factors =1 x 1 = 1
LCM(421,611) = ( 421 × 611 ) / 1
LCM(421,611) = 257231 / 1
LCM(421,611) = 257231
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FAQs on GCF of Fractions of 222/421, 105/611
1. What is the HCF of 222,105?
The HCF of 222,105 is 3
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 222/421, 105/611?
Answer: GCF of Numerators as per given numbers 222/421, 105/611 is
GCF of Numerators i.e. for 222,105 is 3
LCM of denominators i.e. for 421,611 is 257231.
Thus, GCF of Fractions is 3/257231.Finally, GCF of Fractions for 222/421, 105/611 is 3/257231.