GCF of 38/82, 735/66, 217/618
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 38/82, 735/66, 217/618 i.e 1/278718 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/82, 735/66, 217/618.
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 38/82,735/66,217/618?
Given fractions are 38/82,735/66,217/618
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 38/82,735/66,217/618, numerators are 38,735,217
Denominators are 82,66,618
The GCF of 38,735,217 is 1 .
LCM of 82,66,618 is 278718.
The greatest common factor of 38/82,735/66,217/618 = [GCF of 38,735,217]/[LCM of 82,66,618]= 1/278718
Therefore, the GCF of 38/82,735/66,217/618 is 1/278718.
To find the highest common factor of 38,735,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 38 are 1, 2, 19, 38
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
The factors of 217 are 1, 7, 31, 217
The HCF of 38,735,217 is 1.
Lets's calculate GCF of 38,735,217
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 38,735,217 By Matching Biggest Common Factor Method
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 735
:1,3,5,7,15,21,35,49,105,147,245,735
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 38,735,217 . The biggest common factor number is the GCF number.
So the greatest common factor 38,735,217 is 1.
Lets's calculate LCM of 82,66,618
| 2 | 82, 66, 618 |
| 3 | 41, 33, 309 |
| 41, 11, 103 |
∴ So the LCM of the given numbers is 2 x 3 x 41 x 11 x 103 = 278718
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/278718
Therefore, the GCF of Fractions 38/82,735/66,217/618 is 1/278718
Least Common Multiple of 82,66,618 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 82,66,618 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,66,618) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(82,66,618) x common factors =2 x 6 = 12
LCM(82,66,618) = ( 82 × 66 × 618 ) / 12
LCM(82,66,618) = 3344616 / 12
LCM(82,66,618) = 278718
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FAQs on GCF of Fractions of 38/82, 735/66, 217/618
1. What is the HCF of 38,735,217?
The HCF of 38,735,217 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 38/82, 735/66, 217/618?
Answer: GCF of Numerators as per given numbers 38/82, 735/66, 217/618 is
GCF of Numerators i.e. for 38,735,217 is 1
LCM of denominators i.e. for 82,66,618 is 278718.
Thus, GCF of Fractions is 1/278718.Finally, GCF of Fractions for 38/82, 735/66, 217/618 is 1/278718.