GCF of 462/512, 687/170
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 462/512, 687/170 i.e 3/43520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 462/512, 687/170.
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 462/512,687/170?
Given fractions are 462/512,687/170
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 462/512,687/170, numerators are 462,687
Denominators are 512,170
The GCF of 462,687 is 3 .
LCM of 512,170 is 43520.
The greatest common factor of 462/512,687/170 = [GCF of 462,687]/[LCM of 512,170]= 3/43520
Therefore, the GCF of 462/512,687/170 is 3/43520.
To find the highest common factor of 462,687, we have to find the factors of both numbers and list the highest common factor.
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The factors of 687 are 1, 3, 229, 687
The HCF of 462,687 is 3.
Lets's calculate GCF of 462,687
| 3 | 462, 687 |
| 154, 229 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 462,687 By Matching Biggest Common Factor Method
Now, list down the factors of 462
:1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Now, list down the factors of 687
:1,3,229,687
Greatest Common Factor
We found the factors 462,687 . The biggest common factor number is the GCF number.
So the greatest common factor 462,687 is 3.
Lets's calculate LCM of 512,170
| 2 | 512, 170 |
| 256, 85 |
∴ So the LCM of the given numbers is 2 x 256 x 85 = 43520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/43520
Therefore, the GCF of Fractions 462/512,687/170 is 3/43520
Least Common Multiple of 512,170 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 512,170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,170) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(512,170) x common factors =2 x 1 = 2
LCM(512,170) = ( 512 × 170 ) / 2
LCM(512,170) = 87040 / 2
LCM(512,170) = 43520
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FAQs on GCF of Fractions of 462/512, 687/170
1. What is the HCF of 462,687?
The HCF of 462,687 is 3
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 462/512, 687/170?
Answer: GCF of Numerators as per given numbers 462/512, 687/170 is
GCF of Numerators i.e. for 462,687 is 3
LCM of denominators i.e. for 512,170 is 43520.
Thus, GCF of Fractions is 3/43520.Finally, GCF of Fractions for 462/512, 687/170 is 3/43520.