GCF of 403/22, 689/289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 403/22, 689/289 i.e 13/6358 easily. The following is the detailed procedure to determine the greatest common factor of fractions 403/22, 689/289.
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 403/22,689/289?
Given fractions are 403/22,689/289
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 403/22,689/289, numerators are 403,689
Denominators are 22,289
The GCF of 403,689 is 13 .
LCM of 22,289 is 6358.
The greatest common factor of 403/22,689/289 = [GCF of 403,689]/[LCM of 22,289]= 13/6358
Therefore, the GCF of 403/22,689/289 is 13/6358.
To find the highest common factor of 403,689, we have to find the factors of both numbers and list the highest common factor.
The factors of 403 are 1, 13, 31, 403
The factors of 689 are 1, 13, 53, 689
The HCF of 403,689 is 13.
Lets's calculate GCF of 403,689
| 13 | 403, 689 |
| 31, 53 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 403,689 By Matching Biggest Common Factor Method
Now, list down the factors of 403
:1,13,31,403
Now, list down the factors of 689
:1,13,53,689
Greatest Common Factor
We found the factors 403,689 . The biggest common factor number is the GCF number.
So the greatest common factor 403,689 is 13.
Lets's calculate LCM of 22,289
Given numbers has no common factors except 1. So, there LCM is their product i.e 6358
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/6358
Therefore, the GCF of Fractions 403/22,689/289 is 13/6358
Least Common Multiple of 22,289 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 22,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(22,289) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(22,289) x common factors =1 x 1 = 1
LCM(22,289) = ( 22 × 289 ) / 1
LCM(22,289) = 6358 / 1
LCM(22,289) = 6358
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FAQs on GCF of Fractions of 403/22, 689/289
1. What is the HCF of 403,689?
The HCF of 403,689 is 13
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 403/22, 689/289?
Answer: GCF of Numerators as per given numbers 403/22, 689/289 is
GCF of Numerators i.e. for 403,689 is 13
LCM of denominators i.e. for 22,289 is 6358.
Thus, GCF of Fractions is 13/6358.Finally, GCF of Fractions for 403/22, 689/289 is 13/6358.