GCF of 921/64, 684/458
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 921/64, 684/458 i.e 3/14656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 921/64, 684/458.
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 921/64,684/458?
Given fractions are 921/64,684/458
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 921/64,684/458, numerators are 921,684
Denominators are 64,458
The GCF of 921,684 is 3 .
LCM of 64,458 is 14656.
The greatest common factor of 921/64,684/458 = [GCF of 921,684]/[LCM of 64,458]= 3/14656
Therefore, the GCF of 921/64,684/458 is 3/14656.
To find the highest common factor of 921,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 921 are 1, 3, 307, 921
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 921,684 is 3.
Lets's calculate GCF of 921,684
| 3 | 921, 684 |
| 307, 228 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 921,684 By Matching Biggest Common Factor Method
Now, list down the factors of 921
:1,3,307,921
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 921,684 . The biggest common factor number is the GCF number.
So the greatest common factor 921,684 is 3.
Lets's calculate LCM of 64,458
| 2 | 64, 458 |
| 32, 229 |
∴ So the LCM of the given numbers is 2 x 32 x 229 = 14656
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/14656
Therefore, the GCF of Fractions 921/64,684/458 is 3/14656
Least Common Multiple of 64,458 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 64,458 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,458) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(64,458) x common factors =2 x 1 = 2
LCM(64,458) = ( 64 × 458 ) / 2
LCM(64,458) = 29312 / 2
LCM(64,458) = 14656
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FAQs on GCF of Fractions of 921/64, 684/458
1. What is the HCF of 921,684?
The HCF of 921,684 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 921/64, 684/458?
Answer: GCF of Numerators as per given numbers 921/64, 684/458 is
GCF of Numerators i.e. for 921,684 is 3
LCM of denominators i.e. for 64,458 is 14656.
Thus, GCF of Fractions is 3/14656.Finally, GCF of Fractions for 921/64, 684/458 is 3/14656.