GCF of 212/76, 354/162
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 212/76, 354/162 i.e 2/6156 easily. The following is the detailed procedure to determine the greatest common factor of fractions 212/76, 354/162.
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 212/76,354/162?
Given fractions are 212/76,354/162
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 212/76,354/162, numerators are 212,354
Denominators are 76,162
The GCF of 212,354 is 2 .
LCM of 76,162 is 6156.
The greatest common factor of 212/76,354/162 = [GCF of 212,354]/[LCM of 76,162]= 2/6156
Therefore, the GCF of 212/76,354/162 is 2/6156.
To find the highest common factor of 212,354, we have to find the factors of both numbers and list the highest common factor.
The factors of 212 are 1, 2, 4, 53, 106, 212
The factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354
The HCF of 212,354 is 2.
Lets's calculate GCF of 212,354
| 2 | 212, 354 |
| 106, 177 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 212,354 By Matching Biggest Common Factor Method
Now, list down the factors of 212
:1,2,4,53,106,212
Now, list down the factors of 354
:1,2,3,6,59,118,177,354
Greatest Common Factor
We found the factors 212,354 . The biggest common factor number is the GCF number.
So the greatest common factor 212,354 is 2.
Lets's calculate LCM of 76,162
| 2 | 76, 162 |
| 38, 81 |
∴ So the LCM of the given numbers is 2 x 38 x 81 = 6156
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6156
Therefore, the GCF of Fractions 212/76,354/162 is 2/6156
Least Common Multiple of 76,162 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 76,162 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,162) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(76,162) x common factors =2 x 1 = 2
LCM(76,162) = ( 76 × 162 ) / 2
LCM(76,162) = 12312 / 2
LCM(76,162) = 6156
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 212/76, 354/162
1. What is the HCF of 212,354?
The HCF of 212,354 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 212/76, 354/162?
Answer: GCF of Numerators as per given numbers 212/76, 354/162 is
GCF of Numerators i.e. for 212,354 is 2
LCM of denominators i.e. for 76,162 is 6156.
Thus, GCF of Fractions is 2/6156.Finally, GCF of Fractions for 212/76, 354/162 is 2/6156.