GCF of 9678/434, 5754/932
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9678/434, 5754/932 i.e 6/202244 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9678/434, 5754/932.
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 9678/434,5754/932?
Given fractions are 9678/434,5754/932
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 9678/434,5754/932, numerators are 9678,5754
Denominators are 434,932
The GCF of 9678,5754 is 6 .
LCM of 434,932 is 202244.
The greatest common factor of 9678/434,5754/932 = [GCF of 9678,5754]/[LCM of 434,932]= 6/202244
Therefore, the GCF of 9678/434,5754/932 is 6/202244.
To find the highest common factor of 9678,5754, we have to find the factors of both numbers and list the highest common factor.
The factors of 9678 are 1, 2, 3, 6, 1613, 3226, 4839, 9678
The factors of 5754 are 1, 2, 3, 6, 7, 14, 21, 42, 137, 274, 411, 822, 959, 1918, 2877, 5754
The HCF of 9678,5754 is 6.
Lets's calculate GCF of 9678,5754
| 2 | 9678, 5754 |
| 3 | 4839, 2877 |
| 1613, 959 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 9678,5754 By Matching Biggest Common Factor Method
Now, list down the factors of 9678
:1,2,3,6,1613,3226,4839,9678
Now, list down the factors of 5754
:1,2,3,6,7,14,21,42,137,274,411,822,959,1918,2877,5754
Greatest Common Factor
We found the factors 9678,5754 . The biggest common factor number is the GCF number.
So the greatest common factor 9678,5754 is 6.
Lets's calculate LCM of 434,932
| 2 | 434, 932 |
| 217, 466 |
∴ So the LCM of the given numbers is 2 x 217 x 466 = 202244
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/202244
Therefore, the GCF of Fractions 9678/434,5754/932 is 6/202244
Least Common Multiple of 434,932 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 434,932 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(434,932) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(434,932) x common factors =2 x 1 = 2
LCM(434,932) = ( 434 × 932 ) / 2
LCM(434,932) = 404488 / 2
LCM(434,932) = 202244
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FAQs on GCF of Fractions of 9678/434, 5754/932
1. What is the HCF of 9678,5754?
The HCF of 9678,5754 is 6
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 9678/434, 5754/932?
Answer: GCF of Numerators as per given numbers 9678/434, 5754/932 is
GCF of Numerators i.e. for 9678,5754 is 6
LCM of denominators i.e. for 434,932 is 202244.
Thus, GCF of Fractions is 6/202244.Finally, GCF of Fractions for 9678/434, 5754/932 is 6/202244.