GCF of 1098/408, 7634/3154
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1098/408, 7634/3154 i.e 2/643416 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1098/408, 7634/3154.
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 1098/408,7634/3154?
Given fractions are 1098/408,7634/3154
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 1098/408,7634/3154, numerators are 1098,7634
Denominators are 408,3154
The GCF of 1098,7634 is 2 .
LCM of 408,3154 is 643416.
The greatest common factor of 1098/408,7634/3154 = [GCF of 1098,7634]/[LCM of 408,3154]= 2/643416
Therefore, the GCF of 1098/408,7634/3154 is 2/643416.
To find the highest common factor of 1098,7634, we have to find the factors of both numbers and list the highest common factor.
The factors of 1098 are 1, 2, 3, 6, 9, 18, 61, 122, 183, 366, 549, 1098
The factors of 7634 are 1, 2, 11, 22, 347, 694, 3817, 7634
The HCF of 1098,7634 is 2.
Lets's calculate GCF of 1098,7634
| 2 | 1098, 7634 |
| 549, 3817 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1098,7634 By Matching Biggest Common Factor Method
Now, list down the factors of 1098
:1,2,3,6,9,18,61,122,183,366,549,1098
Now, list down the factors of 7634
:1,2,11,22,347,694,3817,7634
Greatest Common Factor
We found the factors 1098,7634 . The biggest common factor number is the GCF number.
So the greatest common factor 1098,7634 is 2.
Lets's calculate LCM of 408,3154
| 2 | 408, 3154 |
| 204, 1577 |
∴ So the LCM of the given numbers is 2 x 204 x 1577 = 643416
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/643416
Therefore, the GCF of Fractions 1098/408,7634/3154 is 2/643416
Least Common Multiple of 408,3154 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 408,3154 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(408,3154) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(408,3154) x common factors =2 x 1 = 2
LCM(408,3154) = ( 408 × 3154 ) / 2
LCM(408,3154) = 1286832 / 2
LCM(408,3154) = 643416
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FAQs on GCF of Fractions of 1098/408, 7634/3154
1. What is the HCF of 1098,7634?
The HCF of 1098,7634 is 2
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 1098/408, 7634/3154?
Answer: GCF of Numerators as per given numbers 1098/408, 7634/3154 is
GCF of Numerators i.e. for 1098,7634 is 2
LCM of denominators i.e. for 408,3154 is 643416.
Thus, GCF of Fractions is 2/643416.Finally, GCF of Fractions for 1098/408, 7634/3154 is 2/643416.