GCF of 640/342, 720/670
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 640/342, 720/670 i.e 80/114570 easily. The following is the detailed procedure to determine the greatest common factor of fractions 640/342, 720/670.
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 640/342,720/670?
Given fractions are 640/342,720/670
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 640/342,720/670, numerators are 640,720
Denominators are 342,670
The GCF of 640,720 is 80 .
LCM of 342,670 is 114570.
The greatest common factor of 640/342,720/670 = [GCF of 640,720]/[LCM of 342,670]= 80/114570
Therefore, the GCF of 640/342,720/670 is 80/114570.
To find the highest common factor of 640,720, we have to find the factors of both numbers and list the highest common factor.
The factors of 640 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640
The factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
The HCF of 640,720 is 80.
Lets's calculate GCF of 640,720
| 2 | 640, 720 |
| 2 | 320, 360 |
| 2 | 160, 180 |
| 2 | 80, 90 |
| 5 | 40, 45 |
| 8, 9 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 5 = 80
Greatest Common Factor of 640,720 By Matching Biggest Common Factor Method
Now, list down the factors of 640
:1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640
Now, list down the factors of 720
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360,720
Greatest Common Factor
We found the factors 640,720 . The biggest common factor number is the GCF number.
So the greatest common factor 640,720 is 80.
Lets's calculate LCM of 342,670
| 2 | 342, 670 |
| 171, 335 |
∴ So the LCM of the given numbers is 2 x 171 x 335 = 114570
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 80/114570
Therefore, the GCF of Fractions 640/342,720/670 is 80/114570
Least Common Multiple of 342,670 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 342,670 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,670) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(342,670) x common factors =2 x 1 = 2
LCM(342,670) = ( 342 × 670 ) / 2
LCM(342,670) = 229140 / 2
LCM(342,670) = 114570
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FAQs on GCF of Fractions of 640/342, 720/670
1. What is the HCF of 640,720?
The HCF of 640,720 is 80
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 640/342, 720/670?
Answer: GCF of Numerators as per given numbers 640/342, 720/670 is
GCF of Numerators i.e. for 640,720 is 80
LCM of denominators i.e. for 342,670 is 114570.
Thus, GCF of Fractions is 80/114570.Finally, GCF of Fractions for 640/342, 720/670 is 80/114570.