GCF of 106/219, 4730/132
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 106/219, 4730/132 i.e 2/9636 easily. The following is the detailed procedure to determine the greatest common factor of fractions 106/219, 4730/132.
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 106/219,4730/132?
Given fractions are 106/219,4730/132
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 106/219,4730/132, numerators are 106,4730
Denominators are 219,132
The GCF of 106,4730 is 2 .
LCM of 219,132 is 9636.
The greatest common factor of 106/219,4730/132 = [GCF of 106,4730]/[LCM of 219,132]= 2/9636
Therefore, the GCF of 106/219,4730/132 is 2/9636.
To find the highest common factor of 106,4730, we have to find the factors of both numbers and list the highest common factor.
The factors of 106 are 1, 2, 53, 106
The factors of 4730 are 1, 2, 5, 10, 11, 22, 43, 55, 86, 110, 215, 430, 473, 946, 2365, 4730
The HCF of 106,4730 is 2.
Lets's calculate GCF of 106,4730
| 2 | 106, 4730 |
| 53, 2365 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 106,4730 By Matching Biggest Common Factor Method
Now, list down the factors of 106
:1,2,53,106
Now, list down the factors of 4730
:1,2,5,10,11,22,43,55,86,110,215,430,473,946,2365,4730
Greatest Common Factor
We found the factors 106,4730 . The biggest common factor number is the GCF number.
So the greatest common factor 106,4730 is 2.
Lets's calculate LCM of 219,132
| 3 | 219, 132 |
| 73, 44 |
∴ So the LCM of the given numbers is 3 x 73 x 44 = 9636
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/9636
Therefore, the GCF of Fractions 106/219,4730/132 is 2/9636
Least Common Multiple of 219,132 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 219,132 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,132) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(219,132) x common factors =3 x 1 = 3
LCM(219,132) = ( 219 × 132 ) / 3
LCM(219,132) = 28908 / 3
LCM(219,132) = 9636
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FAQs on GCF of Fractions of 106/219, 4730/132
1. What is the HCF of 106,4730?
The HCF of 106,4730 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 106/219, 4730/132?
Answer: GCF of Numerators as per given numbers 106/219, 4730/132 is
GCF of Numerators i.e. for 106,4730 is 2
LCM of denominators i.e. for 219,132 is 9636.
Thus, GCF of Fractions is 2/9636.Finally, GCF of Fractions for 106/219, 4730/132 is 2/9636.