GCF of 523/74, 398/84, 672/512
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 523/74, 398/84, 672/512 i.e 1/397824 easily. The following is the detailed procedure to determine the greatest common factor of fractions 523/74, 398/84, 672/512.
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 523/74,398/84,672/512?
Given fractions are 523/74,398/84,672/512
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 523/74,398/84,672/512, numerators are 523,398,672
Denominators are 74,84,512
The GCF of 523,398,672 is 1 .
LCM of 74,84,512 is 397824.
The greatest common factor of 523/74,398/84,672/512 = [GCF of 523,398,672]/[LCM of 74,84,512]= 1/397824
Therefore, the GCF of 523/74,398/84,672/512 is 1/397824.
To find the highest common factor of 523,398,672, we have to find the factors of both numbers and list the highest common factor.
The factors of 523 are 1, 523
The factors of 398 are 1, 2, 199, 398
The factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672
The HCF of 523,398,672 is 1.
Lets's calculate GCF of 523,398,672
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 523,398,672 By Matching Biggest Common Factor Method
Now, list down the factors of 523
:1,523
Now, list down the factors of 398
:1,2,199,398
Now, list down the factors of 672
:1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,56,84,96,112,168,224,336,672
Greatest Common Factor
We found the factors 523,398,672 . The biggest common factor number is the GCF number.
So the greatest common factor 523,398,672 is 1.
Lets's calculate LCM of 74,84,512
| 2 | 74, 84, 512 |
| 2 | 37, 42, 256 |
| 37, 21, 128 |
∴ So the LCM of the given numbers is 2 x 2 x 37 x 21 x 128 = 397824
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/397824
Therefore, the GCF of Fractions 523/74,398/84,672/512 is 1/397824
Least Common Multiple of 74,84,512 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 74,84,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,84,512) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(74,84,512) x common factors =2 x 4 = 8
LCM(74,84,512) = ( 74 × 84 × 512 ) / 8
LCM(74,84,512) = 3182592 / 8
LCM(74,84,512) = 397824
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FAQs on GCF of Fractions of 523/74, 398/84, 672/512
1. What is the HCF of 523,398,672?
The HCF of 523,398,672 is 1
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 523/74, 398/84, 672/512?
Answer: GCF of Numerators as per given numbers 523/74, 398/84, 672/512 is
GCF of Numerators i.e. for 523,398,672 is 1
LCM of denominators i.e. for 74,84,512 is 397824.
Thus, GCF of Fractions is 1/397824.Finally, GCF of Fractions for 523/74, 398/84, 672/512 is 1/397824.