GCF of 640/70, 416/582
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 640/70, 416/582 i.e 32/20370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 640/70, 416/582.
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 640/70,416/582?
Given fractions are 640/70,416/582
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 640/70,416/582, numerators are 640,416
Denominators are 70,582
The GCF of 640,416 is 32 .
LCM of 70,582 is 20370.
The greatest common factor of 640/70,416/582 = [GCF of 640,416]/[LCM of 70,582]= 32/20370
Therefore, the GCF of 640/70,416/582 is 32/20370.
To find the highest common factor of 640,416, 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 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The HCF of 640,416 is 32.
Lets's calculate GCF of 640,416
| 2 | 640, 416 |
| 2 | 320, 208 |
| 2 | 160, 104 |
| 2 | 80, 52 |
| 2 | 40, 26 |
| 20, 13 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 640,416 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 416
:1,2,4,8,13,16,26,32,52,104,208,416
Greatest Common Factor
We found the factors 640,416 . The biggest common factor number is the GCF number.
So the greatest common factor 640,416 is 32.
Lets's calculate LCM of 70,582
| 2 | 70, 582 |
| 35, 291 |
∴ So the LCM of the given numbers is 2 x 35 x 291 = 20370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/20370
Therefore, the GCF of Fractions 640/70,416/582 is 32/20370
Least Common Multiple of 70,582 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 70,582 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,582) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(70,582) x common factors =2 x 1 = 2
LCM(70,582) = ( 70 × 582 ) / 2
LCM(70,582) = 40740 / 2
LCM(70,582) = 20370
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FAQs on GCF of Fractions of 640/70, 416/582
1. What is the HCF of 640,416?
The HCF of 640,416 is 32
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 640/70, 416/582?
Answer: GCF of Numerators as per given numbers 640/70, 416/582 is
GCF of Numerators i.e. for 640,416 is 32
LCM of denominators i.e. for 70,582 is 20370.
Thus, GCF of Fractions is 32/20370.Finally, GCF of Fractions for 640/70, 416/582 is 32/20370.