GCF of 428/462, 321/667
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 428/462, 321/667 i.e 107/308154 easily. The following is the detailed procedure to determine the greatest common factor of fractions 428/462, 321/667.
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 428/462,321/667?
Given fractions are 428/462,321/667
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 428/462,321/667, numerators are 428,321
Denominators are 462,667
The GCF of 428,321 is 107 .
LCM of 462,667 is 308154.
The greatest common factor of 428/462,321/667 = [GCF of 428,321]/[LCM of 462,667]= 107/308154
Therefore, the GCF of 428/462,321/667 is 107/308154.
To find the highest common factor of 428,321, we have to find the factors of both numbers and list the highest common factor.
The factors of 428 are 1, 2, 4, 107, 214, 428
The factors of 321 are 1, 3, 107, 321
The HCF of 428,321 is 107.
Lets's calculate GCF of 428,321
| 107 | 428, 321 |
| 4, 3 |
∴ So the GCF of the given numbers is 107 = 107
Greatest Common Factor of 428,321 By Matching Biggest Common Factor Method
Now, list down the factors of 428
:1,2,4,107,214,428
Now, list down the factors of 321
:1,3,107,321
Greatest Common Factor
We found the factors 428,321 . The biggest common factor number is the GCF number.
So the greatest common factor 428,321 is 107.
Lets's calculate LCM of 462,667
Given numbers has no common factors except 1. So, there LCM is their product i.e 308154
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 107/308154
Therefore, the GCF of Fractions 428/462,321/667 is 107/308154
Least Common Multiple of 462,667 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 462,667 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(462,667) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(462,667) x common factors =1 x 1 = 1
LCM(462,667) = ( 462 × 667 ) / 1
LCM(462,667) = 308154 / 1
LCM(462,667) = 308154
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FAQs on GCF of Fractions of 428/462, 321/667
1. What is the HCF of 428,321?
The HCF of 428,321 is 107
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 428/462, 321/667?
Answer: GCF of Numerators as per given numbers 428/462, 321/667 is
GCF of Numerators i.e. for 428,321 is 107
LCM of denominators i.e. for 462,667 is 308154.
Thus, GCF of Fractions is 107/308154.Finally, GCF of Fractions for 428/462, 321/667 is 107/308154.