GCF of 80/324, 1302/1412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 80/324, 1302/1412 i.e 2/114372 easily. The following is the detailed procedure to determine the greatest common factor of fractions 80/324, 1302/1412.
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 80/324,1302/1412?
Given fractions are 80/324,1302/1412
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 80/324,1302/1412, numerators are 80,1302
Denominators are 324,1412
The GCF of 80,1302 is 2 .
LCM of 324,1412 is 114372.
The greatest common factor of 80/324,1302/1412 = [GCF of 80,1302]/[LCM of 324,1412]= 2/114372
Therefore, the GCF of 80/324,1302/1412 is 2/114372.
To find the highest common factor of 80,1302, we have to find the factors of both numbers and list the highest common factor.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 1302 are 1, 2, 3, 6, 7, 14, 21, 31, 42, 62, 93, 186, 217, 434, 651, 1302
The HCF of 80,1302 is 2.
Lets's calculate GCF of 80,1302
| 2 | 80, 1302 |
| 40, 651 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 80,1302 By Matching Biggest Common Factor Method
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 1302
:1,2,3,6,7,14,21,31,42,62,93,186,217,434,651,1302
Greatest Common Factor
We found the factors 80,1302 . The biggest common factor number is the GCF number.
So the greatest common factor 80,1302 is 2.
Lets's calculate LCM of 324,1412
| 2 | 324, 1412 |
| 2 | 162, 706 |
| 81, 353 |
∴ So the LCM of the given numbers is 2 x 2 x 81 x 353 = 114372
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/114372
Therefore, the GCF of Fractions 80/324,1302/1412 is 2/114372
Least Common Multiple of 324,1412 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 324,1412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(324,1412) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(324,1412) x common factors =4 x 1 = 4
LCM(324,1412) = ( 324 × 1412 ) / 4
LCM(324,1412) = 457488 / 4
LCM(324,1412) = 114372
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FAQs on GCF of Fractions of 80/324, 1302/1412
1. What is the HCF of 80,1302?
The HCF of 80,1302 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 80/324, 1302/1412?
Answer: GCF of Numerators as per given numbers 80/324, 1302/1412 is
GCF of Numerators i.e. for 80,1302 is 2
LCM of denominators i.e. for 324,1412 is 114372.
Thus, GCF of Fractions is 2/114372.Finally, GCF of Fractions for 80/324, 1302/1412 is 2/114372.