GCF of 416/783, 512/840
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 416/783, 512/840 i.e 32/219240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/783, 512/840.
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 416/783,512/840?
Given fractions are 416/783,512/840
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 416/783,512/840, numerators are 416,512
Denominators are 783,840
The GCF of 416,512 is 32 .
LCM of 783,840 is 219240.
The greatest common factor of 416/783,512/840 = [GCF of 416,512]/[LCM of 783,840]= 32/219240
Therefore, the GCF of 416/783,512/840 is 32/219240.
To find the highest common factor of 416,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 416,512 is 32.
Lets's calculate GCF of 416,512
| 2 | 416, 512 |
| 2 | 208, 256 |
| 2 | 104, 128 |
| 2 | 52, 64 |
| 2 | 26, 32 |
| 13, 16 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 416,512 By Matching Biggest Common Factor Method
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 416,512 . The biggest common factor number is the GCF number.
So the greatest common factor 416,512 is 32.
Lets's calculate LCM of 783,840
| 3 | 783, 840 |
| 261, 280 |
∴ So the LCM of the given numbers is 3 x 261 x 280 = 219240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/219240
Therefore, the GCF of Fractions 416/783,512/840 is 32/219240
Least Common Multiple of 783,840 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 783,840 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(783,840) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(783,840) x common factors =3 x 1 = 3
LCM(783,840) = ( 783 × 840 ) / 3
LCM(783,840) = 657720 / 3
LCM(783,840) = 219240
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FAQs on GCF of Fractions of 416/783, 512/840
1. What is the HCF of 416,512?
The HCF of 416,512 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 416/783, 512/840?
Answer: GCF of Numerators as per given numbers 416/783, 512/840 is
GCF of Numerators i.e. for 416,512 is 32
LCM of denominators i.e. for 783,840 is 219240.
Thus, GCF of Fractions is 32/219240.Finally, GCF of Fractions for 416/783, 512/840 is 32/219240.