GCF of 829/51, 698/122
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 829/51, 698/122 i.e 1/6222 easily. The following is the detailed procedure to determine the greatest common factor of fractions 829/51, 698/122.
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 829/51,698/122?
Given fractions are 829/51,698/122
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 829/51,698/122, numerators are 829,698
Denominators are 51,122
The GCF of 829,698 is 1 .
LCM of 51,122 is 6222.
The greatest common factor of 829/51,698/122 = [GCF of 829,698]/[LCM of 51,122]= 1/6222
Therefore, the GCF of 829/51,698/122 is 1/6222.
To find the highest common factor of 829,698, we have to find the factors of both numbers and list the highest common factor.
The factors of 829 are 1, 829
The factors of 698 are 1, 2, 349, 698
The HCF of 829,698 is 1.
Lets's calculate GCF of 829,698
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 829,698 By Matching Biggest Common Factor Method
Now, list down the factors of 829
:1,829
Now, list down the factors of 698
:1,2,349,698
Greatest Common Factor
We found the factors 829,698 . The biggest common factor number is the GCF number.
So the greatest common factor 829,698 is 1.
Lets's calculate LCM of 51,122
Given numbers has no common factors except 1. So, there LCM is their product i.e 6222
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6222
Therefore, the GCF of Fractions 829/51,698/122 is 1/6222
Least Common Multiple of 51,122 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 51,122 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,122) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(51,122) x common factors =1 x 1 = 1
LCM(51,122) = ( 51 × 122 ) / 1
LCM(51,122) = 6222 / 1
LCM(51,122) = 6222
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FAQs on GCF of Fractions of 829/51, 698/122
1. What is the HCF of 829,698?
The HCF of 829,698 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 829/51, 698/122?
Answer: GCF of Numerators as per given numbers 829/51, 698/122 is
GCF of Numerators i.e. for 829,698 is 1
LCM of denominators i.e. for 51,122 is 6222.
Thus, GCF of Fractions is 1/6222.Finally, GCF of Fractions for 829/51, 698/122 is 1/6222.