GCF of 490/61, 245/82, 700/19
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 490/61, 245/82, 700/19 i.e 35/95038 easily. The following is the detailed procedure to determine the greatest common factor of fractions 490/61, 245/82, 700/19.
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 490/61,245/82,700/19?
Given fractions are 490/61,245/82,700/19
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 490/61,245/82,700/19, numerators are 490,245,700
Denominators are 61,82,19
The GCF of 490,245,700 is 35 .
LCM of 61,82,19 is 95038.
The greatest common factor of 490/61,245/82,700/19 = [GCF of 490,245,700]/[LCM of 61,82,19]= 35/95038
Therefore, the GCF of 490/61,245/82,700/19 is 35/95038.
To find the highest common factor of 490,245,700, 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 245 are 1, 5, 7, 35, 49, 245
The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700
The HCF of 490,245,700 is 35.
Lets's calculate GCF of 490,245,700
| 5 | 490, 245, 700 |
| 7 | 98, 49, 140 |
| 14, 7, 20 |
∴ So the GCF of the given numbers is 5 x 7 = 35
Greatest Common Factor of 490,245,700 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 245
:1,5,7,35,49,245
Now, list down the factors of 700
:1,2,4,5,7,10,14,20,25,28,35,50,70,100,140,175,350,700
Greatest Common Factor
We found the factors 490,245,700 . The biggest common factor number is the GCF number.
So the greatest common factor 490,245,700 is 35.
Lets's calculate LCM of 61,82,19
Given numbers has no common factors except 1. So, there LCM is their product i.e 95038
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 35/95038
Therefore, the GCF of Fractions 490/61,245/82,700/19 is 35/95038
Least Common Multiple of 61,82,19 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 61,82,19 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(61,82,19) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(61,82,19) x common factors =1 x 1 = 1
LCM(61,82,19) = ( 61 × 82 × 19 ) / 1
LCM(61,82,19) = 95038 / 1
LCM(61,82,19) = 95038
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 490/61, 245/82, 700/19
1. What is the HCF of 490,245,700?
The HCF of 490,245,700 is 35
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 490/61, 245/82, 700/19?
Answer: GCF of Numerators as per given numbers 490/61, 245/82, 700/19 is
GCF of Numerators i.e. for 490,245,700 is 35
LCM of denominators i.e. for 61,82,19 is 95038.
Thus, GCF of Fractions is 35/95038.Finally, GCF of Fractions for 490/61, 245/82, 700/19 is 35/95038.