GCF of 456/82, 219/106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 456/82, 219/106 i.e 3/4346 easily. The following is the detailed procedure to determine the greatest common factor of fractions 456/82, 219/106.
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 456/82,219/106?
Given fractions are 456/82,219/106
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 456/82,219/106, numerators are 456,219
Denominators are 82,106
The GCF of 456,219 is 3 .
LCM of 82,106 is 4346.
The greatest common factor of 456/82,219/106 = [GCF of 456,219]/[LCM of 82,106]= 3/4346
Therefore, the GCF of 456/82,219/106 is 3/4346.
To find the highest common factor of 456,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The factors of 219 are 1, 3, 73, 219
The HCF of 456,219 is 3.
Lets's calculate GCF of 456,219
| 3 | 456, 219 |
| 152, 73 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 456,219 By Matching Biggest Common Factor Method
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 456,219 . The biggest common factor number is the GCF number.
So the greatest common factor 456,219 is 3.
Lets's calculate LCM of 82,106
| 2 | 82, 106 |
| 41, 53 |
∴ So the LCM of the given numbers is 2 x 41 x 53 = 4346
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/4346
Therefore, the GCF of Fractions 456/82,219/106 is 3/4346
Least Common Multiple of 82,106 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 82,106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,106) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(82,106) x common factors =2 x 1 = 2
LCM(82,106) = ( 82 × 106 ) / 2
LCM(82,106) = 8692 / 2
LCM(82,106) = 4346
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FAQs on GCF of Fractions of 456/82, 219/106
1. What is the HCF of 456,219?
The HCF of 456,219 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 456/82, 219/106?
Answer: GCF of Numerators as per given numbers 456/82, 219/106 is
GCF of Numerators i.e. for 456,219 is 3
LCM of denominators i.e. for 82,106 is 4346.
Thus, GCF of Fractions is 3/4346.Finally, GCF of Fractions for 456/82, 219/106 is 3/4346.