GCF of 490/36, 616/1709
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 490/36, 616/1709 i.e 14/61524 easily. The following is the detailed procedure to determine the greatest common factor of fractions 490/36, 616/1709.
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 490/36,616/1709?
Given fractions are 490/36,616/1709
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 490/36,616/1709, numerators are 490,616
Denominators are 36,1709
The GCF of 490,616 is 14 .
LCM of 36,1709 is 61524.
The greatest common factor of 490/36,616/1709 = [GCF of 490,616]/[LCM of 36,1709]= 14/61524
Therefore, the GCF of 490/36,616/1709 is 14/61524.
To find the highest common factor of 490,616, we have to find the factors of both numbers and list the highest common factor.
The factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490
The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616
The HCF of 490,616 is 14.
Lets's calculate GCF of 490,616
| 2 | 490, 616 |
| 7 | 245, 308 |
| 35, 44 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 490,616 By Matching Biggest Common Factor Method
Now, list down the factors of 490
:1,2,5,7,10,14,35,49,70,98,245,490
Now, list down the factors of 616
:1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616
Greatest Common Factor
We found the factors 490,616 . The biggest common factor number is the GCF number.
So the greatest common factor 490,616 is 14.
Lets's calculate LCM of 36,1709
Given numbers has no common factors except 1. So, there LCM is their product i.e 61524
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/61524
Therefore, the GCF of Fractions 490/36,616/1709 is 14/61524
Least Common Multiple of 36,1709 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 36,1709 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,1709) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(36,1709) x common factors =1 x 1 = 1
LCM(36,1709) = ( 36 × 1709 ) / 1
LCM(36,1709) = 61524 / 1
LCM(36,1709) = 61524
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FAQs on GCF of Fractions of 490/36, 616/1709
1. What is the HCF of 490,616?
The HCF of 490,616 is 14
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 490/36, 616/1709?
Answer: GCF of Numerators as per given numbers 490/36, 616/1709 is
GCF of Numerators i.e. for 490,616 is 14
LCM of denominators i.e. for 36,1709 is 61524.
Thus, GCF of Fractions is 14/61524.Finally, GCF of Fractions for 490/36, 616/1709 is 14/61524.