GCF of 9738/854, 3822/6182
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9738/854, 3822/6182 i.e 6/2639714 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9738/854, 3822/6182.
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 9738/854,3822/6182?
Given fractions are 9738/854,3822/6182
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 9738/854,3822/6182, numerators are 9738,3822
Denominators are 854,6182
The GCF of 9738,3822 is 6 .
LCM of 854,6182 is 2639714.
The greatest common factor of 9738/854,3822/6182 = [GCF of 9738,3822]/[LCM of 854,6182]= 6/2639714
Therefore, the GCF of 9738/854,3822/6182 is 6/2639714.
To find the highest common factor of 9738,3822, we have to find the factors of both numbers and list the highest common factor.
The factors of 9738 are 1, 2, 3, 6, 9, 18, 541, 1082, 1623, 3246, 4869, 9738
The factors of 3822 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 49, 78, 91, 98, 147, 182, 273, 294, 546, 637, 1274, 1911, 3822
The HCF of 9738,3822 is 6.
Lets's calculate GCF of 9738,3822
| 2 | 9738, 3822 |
| 3 | 4869, 1911 |
| 1623, 637 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 9738,3822 By Matching Biggest Common Factor Method
Now, list down the factors of 9738
:1,2,3,6,9,18,541,1082,1623,3246,4869,9738
Now, list down the factors of 3822
:1,2,3,6,7,13,14,21,26,39,42,49,78,91,98,147,182,273,294,546,637,1274,1911,3822
Greatest Common Factor
We found the factors 9738,3822 . The biggest common factor number is the GCF number.
So the greatest common factor 9738,3822 is 6.
Lets's calculate LCM of 854,6182
| 2 | 854, 6182 |
| 427, 3091 |
∴ So the LCM of the given numbers is 2 x 427 x 3091 = 2639714
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/2639714
Therefore, the GCF of Fractions 9738/854,3822/6182 is 6/2639714
Least Common Multiple of 854,6182 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 854,6182 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(854,6182) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(854,6182) x common factors =2 x 1 = 2
LCM(854,6182) = ( 854 × 6182 ) / 2
LCM(854,6182) = 5279428 / 2
LCM(854,6182) = 2639714
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FAQs on GCF of Fractions of 9738/854, 3822/6182
1. What is the HCF of 9738,3822?
The HCF of 9738,3822 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 9738/854, 3822/6182?
Answer: GCF of Numerators as per given numbers 9738/854, 3822/6182 is
GCF of Numerators i.e. for 9738,3822 is 6
LCM of denominators i.e. for 854,6182 is 2639714.
Thus, GCF of Fractions is 6/2639714.Finally, GCF of Fractions for 9738/854, 3822/6182 is 6/2639714.