GCF of 982/35, 402/78, 414/47
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 982/35, 402/78, 414/47 i.e 2/128310 easily. The following is the detailed procedure to determine the greatest common factor of fractions 982/35, 402/78, 414/47.
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 982/35,402/78,414/47?
Given fractions are 982/35,402/78,414/47
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 982/35,402/78,414/47, numerators are 982,402,414
Denominators are 35,78,47
The GCF of 982,402,414 is 2 .
LCM of 35,78,47 is 128310.
The greatest common factor of 982/35,402/78,414/47 = [GCF of 982,402,414]/[LCM of 35,78,47]= 2/128310
Therefore, the GCF of 982/35,402/78,414/47 is 2/128310.
To find the highest common factor of 982,402,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 982 are 1, 2, 491, 982
The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 982,402,414 is 2.
Lets's calculate GCF of 982,402,414
| 2 | 982, 402, 414 |
| 491, 201, 207 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 982,402,414 By Matching Biggest Common Factor Method
Now, list down the factors of 982
:1,2,491,982
Now, list down the factors of 402
:1,2,3,6,67,134,201,402
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 982,402,414 . The biggest common factor number is the GCF number.
So the greatest common factor 982,402,414 is 2.
Lets's calculate LCM of 35,78,47
Given numbers has no common factors except 1. So, there LCM is their product i.e 128310
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/128310
Therefore, the GCF of Fractions 982/35,402/78,414/47 is 2/128310
Least Common Multiple of 35,78,47 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 35,78,47 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,78,47) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(35,78,47) x common factors =1 x 1 = 1
LCM(35,78,47) = ( 35 × 78 × 47 ) / 1
LCM(35,78,47) = 128310 / 1
LCM(35,78,47) = 128310
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FAQs on GCF of Fractions of 982/35, 402/78, 414/47
1. What is the HCF of 982,402,414?
The HCF of 982,402,414 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 982/35, 402/78, 414/47?
Answer: GCF of Numerators as per given numbers 982/35, 402/78, 414/47 is
GCF of Numerators i.e. for 982,402,414 is 2
LCM of denominators i.e. for 35,78,47 is 128310.
Thus, GCF of Fractions is 2/128310.Finally, GCF of Fractions for 982/35, 402/78, 414/47 is 2/128310.