GCF of 2698/823, 5822/1259
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2698/823, 5822/1259 i.e 142/1036157 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2698/823, 5822/1259.
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 2698/823,5822/1259?
Given fractions are 2698/823,5822/1259
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 2698/823,5822/1259, numerators are 2698,5822
Denominators are 823,1259
The GCF of 2698,5822 is 142 .
LCM of 823,1259 is 1036157.
The greatest common factor of 2698/823,5822/1259 = [GCF of 2698,5822]/[LCM of 823,1259]= 142/1036157
Therefore, the GCF of 2698/823,5822/1259 is 142/1036157.
To find the highest common factor of 2698,5822, we have to find the factors of both numbers and list the highest common factor.
The factors of 2698 are 1, 2, 19, 38, 71, 142, 1349, 2698
The factors of 5822 are 1, 2, 41, 71, 82, 142, 2911, 5822
The HCF of 2698,5822 is 142.
Lets's calculate GCF of 2698,5822
| 2 | 2698, 5822 |
| 71 | 1349, 2911 |
| 19, 41 |
∴ So the GCF of the given numbers is 2 x 71 = 142
Greatest Common Factor of 2698,5822 By Matching Biggest Common Factor Method
Now, list down the factors of 2698
:1,2,19,38,71,142,1349,2698
Now, list down the factors of 5822
:1,2,41,71,82,142,2911,5822
Greatest Common Factor
We found the factors 2698,5822 . The biggest common factor number is the GCF number.
So the greatest common factor 2698,5822 is 142.
Lets's calculate LCM of 823,1259
Given numbers has no common factors except 1. So, there LCM is their product i.e 1036157
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 142/1036157
Therefore, the GCF of Fractions 2698/823,5822/1259 is 142/1036157
Least Common Multiple of 823,1259 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 823,1259 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(823,1259) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(823,1259) x common factors =1 x 1 = 1
LCM(823,1259) = ( 823 × 1259 ) / 1
LCM(823,1259) = 1036157 / 1
LCM(823,1259) = 1036157
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FAQs on GCF of Fractions of 2698/823, 5822/1259
1. What is the HCF of 2698,5822?
The HCF of 2698,5822 is 142
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 2698/823, 5822/1259?
Answer: GCF of Numerators as per given numbers 2698/823, 5822/1259 is
GCF of Numerators i.e. for 2698,5822 is 142
LCM of denominators i.e. for 823,1259 is 1036157.
Thus, GCF of Fractions is 142/1036157.Finally, GCF of Fractions for 2698/823, 5822/1259 is 142/1036157.