GCF of 675/82, 982/422
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 675/82, 982/422 i.e 1/17302 easily. The following is the detailed procedure to determine the greatest common factor of fractions 675/82, 982/422.
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 675/82,982/422?
Given fractions are 675/82,982/422
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 675/82,982/422, numerators are 675,982
Denominators are 82,422
The GCF of 675,982 is 1 .
LCM of 82,422 is 17302.
The greatest common factor of 675/82,982/422 = [GCF of 675,982]/[LCM of 82,422]= 1/17302
Therefore, the GCF of 675/82,982/422 is 1/17302.
To find the highest common factor of 675,982, we have to find the factors of both numbers and list the highest common factor.
The factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
The factors of 982 are 1, 2, 491, 982
The HCF of 675,982 is 1.
Lets's calculate GCF of 675,982
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 675,982 By Matching Biggest Common Factor Method
Now, list down the factors of 675
:1,3,5,9,15,25,27,45,75,135,225,675
Now, list down the factors of 982
:1,2,491,982
Greatest Common Factor
We found the factors 675,982 . The biggest common factor number is the GCF number.
So the greatest common factor 675,982 is 1.
Lets's calculate LCM of 82,422
| 2 | 82, 422 |
| 41, 211 |
∴ So the LCM of the given numbers is 2 x 41 x 211 = 17302
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17302
Therefore, the GCF of Fractions 675/82,982/422 is 1/17302
Least Common Multiple of 82,422 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 82,422 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,422) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(82,422) x common factors =2 x 1 = 2
LCM(82,422) = ( 82 × 422 ) / 2
LCM(82,422) = 34604 / 2
LCM(82,422) = 17302
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FAQs on GCF of Fractions of 675/82, 982/422
1. What is the HCF of 675,982?
The HCF of 675,982 is 1
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 675/82, 982/422?
Answer: GCF of Numerators as per given numbers 675/82, 982/422 is
GCF of Numerators i.e. for 675,982 is 1
LCM of denominators i.e. for 82,422 is 17302.
Thus, GCF of Fractions is 1/17302.Finally, GCF of Fractions for 675/82, 982/422 is 1/17302.