GCF of 984/31, 698/3417
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 984/31, 698/3417 i.e 2/105927 easily. The following is the detailed procedure to determine the greatest common factor of fractions 984/31, 698/3417.
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 984/31,698/3417?
Given fractions are 984/31,698/3417
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 984/31,698/3417, numerators are 984,698
Denominators are 31,3417
The GCF of 984,698 is 2 .
LCM of 31,3417 is 105927.
The greatest common factor of 984/31,698/3417 = [GCF of 984,698]/[LCM of 31,3417]= 2/105927
Therefore, the GCF of 984/31,698/3417 is 2/105927.
To find the highest common factor of 984,698, we have to find the factors of both numbers and list the highest common factor.
The factors of 984 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984
The factors of 698 are 1, 2, 349, 698
The HCF of 984,698 is 2.
Lets's calculate GCF of 984,698
| 2 | 984, 698 |
| 492, 349 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 984,698 By Matching Biggest Common Factor Method
Now, list down the factors of 984
:1,2,3,4,6,8,12,24,41,82,123,164,246,328,492,984
Now, list down the factors of 698
:1,2,349,698
Greatest Common Factor
We found the factors 984,698 . The biggest common factor number is the GCF number.
So the greatest common factor 984,698 is 2.
Lets's calculate LCM of 31,3417
Given numbers has no common factors except 1. So, there LCM is their product i.e 105927
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/105927
Therefore, the GCF of Fractions 984/31,698/3417 is 2/105927
Least Common Multiple of 31,3417 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 31,3417 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,3417) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,3417) x common factors =1 x 1 = 1
LCM(31,3417) = ( 31 × 3417 ) / 1
LCM(31,3417) = 105927 / 1
LCM(31,3417) = 105927
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FAQs on GCF of Fractions of 984/31, 698/3417
1. What is the HCF of 984,698?
The HCF of 984,698 is 2
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 984/31, 698/3417?
Answer: GCF of Numerators as per given numbers 984/31, 698/3417 is
GCF of Numerators i.e. for 984,698 is 2
LCM of denominators i.e. for 31,3417 is 105927.
Thus, GCF of Fractions is 2/105927.Finally, GCF of Fractions for 984/31, 698/3417 is 2/105927.