GCF of 417/420, 984/341
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 417/420, 984/341 i.e 3/143220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 417/420, 984/341.
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 417/420,984/341?
Given fractions are 417/420,984/341
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 417/420,984/341, numerators are 417,984
Denominators are 420,341
The GCF of 417,984 is 3 .
LCM of 420,341 is 143220.
The greatest common factor of 417/420,984/341 = [GCF of 417,984]/[LCM of 420,341]= 3/143220
Therefore, the GCF of 417/420,984/341 is 3/143220.
To find the highest common factor of 417,984, we have to find the factors of both numbers and list the highest common factor.
The factors of 417 are 1, 3, 139, 417
The factors of 984 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984
The HCF of 417,984 is 3.
Lets's calculate GCF of 417,984
| 3 | 417, 984 |
| 139, 328 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 417,984 By Matching Biggest Common Factor Method
Now, list down the factors of 417
:1,3,139,417
Now, list down the factors of 984
:1,2,3,4,6,8,12,24,41,82,123,164,246,328,492,984
Greatest Common Factor
We found the factors 417,984 . The biggest common factor number is the GCF number.
So the greatest common factor 417,984 is 3.
Lets's calculate LCM of 420,341
Given numbers has no common factors except 1. So, there LCM is their product i.e 143220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/143220
Therefore, the GCF of Fractions 417/420,984/341 is 3/143220
Least Common Multiple of 420,341 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 420,341 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,341) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(420,341) x common factors =1 x 1 = 1
LCM(420,341) = ( 420 × 341 ) / 1
LCM(420,341) = 143220 / 1
LCM(420,341) = 143220
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FAQs on GCF of Fractions of 417/420, 984/341
1. What is the HCF of 417,984?
The HCF of 417,984 is 3
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 417/420, 984/341?
Answer: GCF of Numerators as per given numbers 417/420, 984/341 is
GCF of Numerators i.e. for 417,984 is 3
LCM of denominators i.e. for 420,341 is 143220.
Thus, GCF of Fractions is 3/143220.Finally, GCF of Fractions for 417/420, 984/341 is 3/143220.