GCF of 989/134, 414/491
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 989/134, 414/491 i.e 23/65794 easily. The following is the detailed procedure to determine the greatest common factor of fractions 989/134, 414/491.
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 989/134,414/491?
Given fractions are 989/134,414/491
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 989/134,414/491, numerators are 989,414
Denominators are 134,491
The GCF of 989,414 is 23 .
LCM of 134,491 is 65794.
The greatest common factor of 989/134,414/491 = [GCF of 989,414]/[LCM of 134,491]= 23/65794
Therefore, the GCF of 989/134,414/491 is 23/65794.
To find the highest common factor of 989,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 989 are 1, 23, 43, 989
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 989,414 is 23.
Lets's calculate GCF of 989,414
| 23 | 989, 414 |
| 43, 18 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 989,414 By Matching Biggest Common Factor Method
Now, list down the factors of 989
:1,23,43,989
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 989,414 . The biggest common factor number is the GCF number.
So the greatest common factor 989,414 is 23.
Lets's calculate LCM of 134,491
Given numbers has no common factors except 1. So, there LCM is their product i.e 65794
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/65794
Therefore, the GCF of Fractions 989/134,414/491 is 23/65794
Least Common Multiple of 134,491 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 134,491 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(134,491) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(134,491) x common factors =1 x 1 = 1
LCM(134,491) = ( 134 × 491 ) / 1
LCM(134,491) = 65794 / 1
LCM(134,491) = 65794
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FAQs on GCF of Fractions of 989/134, 414/491
1. What is the HCF of 989,414?
The HCF of 989,414 is 23
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 989/134, 414/491?
Answer: GCF of Numerators as per given numbers 989/134, 414/491 is
GCF of Numerators i.e. for 989,414 is 23
LCM of denominators i.e. for 134,491 is 65794.
Thus, GCF of Fractions is 23/65794.Finally, GCF of Fractions for 989/134, 414/491 is 23/65794.