GCF of 490/821, 975/688
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 490/821, 975/688 i.e 5/564848 easily. The following is the detailed procedure to determine the greatest common factor of fractions 490/821, 975/688.
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 490/821,975/688?
Given fractions are 490/821,975/688
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 490/821,975/688, numerators are 490,975
Denominators are 821,688
The GCF of 490,975 is 5 .
LCM of 821,688 is 564848.
The greatest common factor of 490/821,975/688 = [GCF of 490,975]/[LCM of 821,688]= 5/564848
Therefore, the GCF of 490/821,975/688 is 5/564848.
To find the highest common factor of 490,975, 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 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 490,975 is 5.
Lets's calculate GCF of 490,975
| 5 | 490, 975 |
| 98, 195 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 490,975 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 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 490,975 . The biggest common factor number is the GCF number.
So the greatest common factor 490,975 is 5.
Lets's calculate LCM of 821,688
Given numbers has no common factors except 1. So, there LCM is their product i.e 564848
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/564848
Therefore, the GCF of Fractions 490/821,975/688 is 5/564848
Least Common Multiple of 821,688 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 821,688 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(821,688) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(821,688) x common factors =1 x 1 = 1
LCM(821,688) = ( 821 × 688 ) / 1
LCM(821,688) = 564848 / 1
LCM(821,688) = 564848
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FAQs on GCF of Fractions of 490/821, 975/688
1. What is the HCF of 490,975?
The HCF of 490,975 is 5
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 490/821, 975/688?
Answer: GCF of Numerators as per given numbers 490/821, 975/688 is
GCF of Numerators i.e. for 490,975 is 5
LCM of denominators i.e. for 821,688 is 564848.
Thus, GCF of Fractions is 5/564848.Finally, GCF of Fractions for 490/821, 975/688 is 5/564848.