GCF of 34/61, 982/55, 385/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/61, 982/55, 385/420 i.e 1/281820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/61, 982/55, 385/420.
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 34/61,982/55,385/420?
Given fractions are 34/61,982/55,385/420
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 34/61,982/55,385/420, numerators are 34,982,385
Denominators are 61,55,420
The GCF of 34,982,385 is 1 .
LCM of 61,55,420 is 281820.
The greatest common factor of 34/61,982/55,385/420 = [GCF of 34,982,385]/[LCM of 61,55,420]= 1/281820
Therefore, the GCF of 34/61,982/55,385/420 is 1/281820.
To find the highest common factor of 34,982,385, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 982 are 1, 2, 491, 982
The factors of 385 are 1, 5, 7, 11, 35, 55, 77, 385
The HCF of 34,982,385 is 1.
Lets's calculate GCF of 34,982,385
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 34,982,385 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 982
:1,2,491,982
Now, list down the factors of 385
:1,5,7,11,35,55,77,385
Greatest Common Factor
We found the factors 34,982,385 . The biggest common factor number is the GCF number.
So the greatest common factor 34,982,385 is 1.
Lets's calculate LCM of 61,55,420
| 5 | 61, 55, 420 |
| 61, 11, 84 |
∴ So the LCM of the given numbers is 5 x 61 x 11 x 84 = 281820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/281820
Therefore, the GCF of Fractions 34/61,982/55,385/420 is 1/281820
Least Common Multiple of 61,55,420 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 61,55,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(61,55,420) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(61,55,420) x common factors =1 x 5 = 5
LCM(61,55,420) = ( 61 × 55 × 420 ) / 5
LCM(61,55,420) = 1409100 / 5
LCM(61,55,420) = 281820
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FAQs on GCF of Fractions of 34/61, 982/55, 385/420
1. What is the HCF of 34,982,385?
The HCF of 34,982,385 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 34/61, 982/55, 385/420?
Answer: GCF of Numerators as per given numbers 34/61, 982/55, 385/420 is
GCF of Numerators i.e. for 34,982,385 is 1
LCM of denominators i.e. for 61,55,420 is 281820.
Thus, GCF of Fractions is 1/281820.Finally, GCF of Fractions for 34/61, 982/55, 385/420 is 1/281820.