GCF of 754/85, 512/865
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 754/85, 512/865 i.e 2/14705 easily. The following is the detailed procedure to determine the greatest common factor of fractions 754/85, 512/865.
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 754/85,512/865?
Given fractions are 754/85,512/865
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 754/85,512/865, numerators are 754,512
Denominators are 85,865
The GCF of 754,512 is 2 .
LCM of 85,865 is 14705.
The greatest common factor of 754/85,512/865 = [GCF of 754,512]/[LCM of 85,865]= 2/14705
Therefore, the GCF of 754/85,512/865 is 2/14705.
To find the highest common factor of 754,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 754 are 1, 2, 13, 26, 29, 58, 377, 754
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 754,512 is 2.
Lets's calculate GCF of 754,512
| 2 | 754, 512 |
| 377, 256 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 754,512 By Matching Biggest Common Factor Method
Now, list down the factors of 754
:1,2,13,26,29,58,377,754
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 754,512 . The biggest common factor number is the GCF number.
So the greatest common factor 754,512 is 2.
Lets's calculate LCM of 85,865
| 5 | 85, 865 |
| 17, 173 |
∴ So the LCM of the given numbers is 5 x 17 x 173 = 14705
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/14705
Therefore, the GCF of Fractions 754/85,512/865 is 2/14705
Least Common Multiple of 85,865 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 85,865 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,865) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(85,865) x common factors =5 x 1 = 5
LCM(85,865) = ( 85 × 865 ) / 5
LCM(85,865) = 73525 / 5
LCM(85,865) = 14705
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FAQs on GCF of Fractions of 754/85, 512/865
1. What is the HCF of 754,512?
The HCF of 754,512 is 2
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 754/85, 512/865?
Answer: GCF of Numerators as per given numbers 754/85, 512/865 is
GCF of Numerators i.e. for 754,512 is 2
LCM of denominators i.e. for 85,865 is 14705.
Thus, GCF of Fractions is 2/14705.Finally, GCF of Fractions for 754/85, 512/865 is 2/14705.