GCF of 423/765, 684/628
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 423/765, 684/628 i.e 9/480420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 423/765, 684/628.
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 423/765,684/628?
Given fractions are 423/765,684/628
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 423/765,684/628, numerators are 423,684
Denominators are 765,628
The GCF of 423,684 is 9 .
LCM of 765,628 is 480420.
The greatest common factor of 423/765,684/628 = [GCF of 423,684]/[LCM of 765,628]= 9/480420
Therefore, the GCF of 423/765,684/628 is 9/480420.
To find the highest common factor of 423,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 423 are 1, 3, 9, 47, 141, 423
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 423,684 is 9.
Lets's calculate GCF of 423,684
| 3 | 423, 684 |
| 3 | 141, 228 |
| 47, 76 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 423,684 By Matching Biggest Common Factor Method
Now, list down the factors of 423
:1,3,9,47,141,423
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 423,684 . The biggest common factor number is the GCF number.
So the greatest common factor 423,684 is 9.
Lets's calculate LCM of 765,628
Given numbers has no common factors except 1. So, there LCM is their product i.e 480420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/480420
Therefore, the GCF of Fractions 423/765,684/628 is 9/480420
Least Common Multiple of 765,628 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 765,628 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(765,628) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(765,628) x common factors =1 x 1 = 1
LCM(765,628) = ( 765 × 628 ) / 1
LCM(765,628) = 480420 / 1
LCM(765,628) = 480420
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FAQs on GCF of Fractions of 423/765, 684/628
1. What is the HCF of 423,684?
The HCF of 423,684 is 9
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 423/765, 684/628?
Answer: GCF of Numerators as per given numbers 423/765, 684/628 is
GCF of Numerators i.e. for 423,684 is 9
LCM of denominators i.e. for 765,628 is 480420.
Thus, GCF of Fractions is 9/480420.Finally, GCF of Fractions for 423/765, 684/628 is 9/480420.