GCF of 705/130, 7200/7346
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 705/130, 7200/7346 i.e 15/477490 easily. The following is the detailed procedure to determine the greatest common factor of fractions 705/130, 7200/7346.
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 705/130,7200/7346?
Given fractions are 705/130,7200/7346
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 705/130,7200/7346, numerators are 705,7200
Denominators are 130,7346
The GCF of 705,7200 is 15 .
LCM of 130,7346 is 477490.
The greatest common factor of 705/130,7200/7346 = [GCF of 705,7200]/[LCM of 130,7346]= 15/477490
Therefore, the GCF of 705/130,7200/7346 is 15/477490.
To find the highest common factor of 705,7200, we have to find the factors of both numbers and list the highest common factor.
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The factors of 7200 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 200, 225, 240, 288, 300, 360, 400, 450, 480, 600, 720, 800, 900, 1200, 1440, 1800, 2400, 3600, 7200
The HCF of 705,7200 is 15.
Lets's calculate GCF of 705,7200
| 3 | 705, 7200 |
| 5 | 235, 2400 |
| 47, 480 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 705,7200 By Matching Biggest Common Factor Method
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Now, list down the factors of 7200
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,32,36,40,45,48,50,60,72,75,80,90,96,100,120,144,150,160,180,200,225,240,288,300,360,400,450,480,600,720,800,900,1200,1440,1800,2400,3600,7200
Greatest Common Factor
We found the factors 705,7200 . The biggest common factor number is the GCF number.
So the greatest common factor 705,7200 is 15.
Lets's calculate LCM of 130,7346
| 2 | 130, 7346 |
| 65, 3673 |
∴ So the LCM of the given numbers is 2 x 65 x 3673 = 477490
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/477490
Therefore, the GCF of Fractions 705/130,7200/7346 is 15/477490
Least Common Multiple of 130,7346 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 130,7346 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(130,7346) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(130,7346) x common factors =2 x 1 = 2
LCM(130,7346) = ( 130 × 7346 ) / 2
LCM(130,7346) = 954980 / 2
LCM(130,7346) = 477490
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 705/130, 7200/7346
1. What is the HCF of 705,7200?
The HCF of 705,7200 is 15
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 705/130, 7200/7346?
Answer: GCF of Numerators as per given numbers 705/130, 7200/7346 is
GCF of Numerators i.e. for 705,7200 is 15
LCM of denominators i.e. for 130,7346 is 477490.
Thus, GCF of Fractions is 15/477490.Finally, GCF of Fractions for 705/130, 7200/7346 is 15/477490.