GCF of 544/76, 512/755
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 544/76, 512/755 i.e 32/57380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 544/76, 512/755.
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 544/76,512/755?
Given fractions are 544/76,512/755
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 544/76,512/755, numerators are 544,512
Denominators are 76,755
The GCF of 544,512 is 32 .
LCM of 76,755 is 57380.
The greatest common factor of 544/76,512/755 = [GCF of 544,512]/[LCM of 76,755]= 32/57380
Therefore, the GCF of 544/76,512/755 is 32/57380.
To find the highest common factor of 544,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 544 are 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 544,512 is 32.
Lets's calculate GCF of 544,512
| 2 | 544, 512 |
| 2 | 272, 256 |
| 2 | 136, 128 |
| 2 | 68, 64 |
| 2 | 34, 32 |
| 17, 16 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 544,512 By Matching Biggest Common Factor Method
Now, list down the factors of 544
:1,2,4,8,16,17,32,34,68,136,272,544
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 544,512 . The biggest common factor number is the GCF number.
So the greatest common factor 544,512 is 32.
Lets's calculate LCM of 76,755
Given numbers has no common factors except 1. So, there LCM is their product i.e 57380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/57380
Therefore, the GCF of Fractions 544/76,512/755 is 32/57380
Least Common Multiple of 76,755 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 76,755 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,755) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(76,755) x common factors =1 x 1 = 1
LCM(76,755) = ( 76 × 755 ) / 1
LCM(76,755) = 57380 / 1
LCM(76,755) = 57380
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FAQs on GCF of Fractions of 544/76, 512/755
1. What is the HCF of 544,512?
The HCF of 544,512 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 544/76, 512/755?
Answer: GCF of Numerators as per given numbers 544/76, 512/755 is
GCF of Numerators i.e. for 544,512 is 32
LCM of denominators i.e. for 76,755 is 57380.
Thus, GCF of Fractions is 32/57380.Finally, GCF of Fractions for 544/76, 512/755 is 32/57380.