GCF of 278/217, 832/217
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 278/217, 832/217 i.e 2/217 easily. The following is the detailed procedure to determine the greatest common factor of fractions 278/217, 832/217.
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 278/217,832/217?
Given fractions are 278/217,832/217
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 278/217,832/217, numerators are 278,832
Denominators are 217,217
The GCF of 278,832 is 2 .
LCM of 217,217 is 217.
The greatest common factor of 278/217,832/217 = [GCF of 278,832]/[LCM of 217,217]= 2/217
Therefore, the GCF of 278/217,832/217 is 2/217.
To find the highest common factor of 278,832, we have to find the factors of both numbers and list the highest common factor.
The factors of 278 are 1, 2, 139, 278
The factors of 832 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832
The HCF of 278,832 is 2.
Lets's calculate GCF of 278,832
| 2 | 278, 832 |
| 139, 416 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 278,832 By Matching Biggest Common Factor Method
Now, list down the factors of 278
:1,2,139,278
Now, list down the factors of 832
:1,2,4,8,13,16,26,32,52,64,104,208,416,832
Greatest Common Factor
We found the factors 278,832 . The biggest common factor number is the GCF number.
So the greatest common factor 278,832 is 2.
Lets's calculate LCM of 217,217
| 7 | 217, 217 |
| 31 | 31, 31 |
| 1, 1 |
∴ So the LCM of the given numbers is 7 x 31 x 1 x 1 = 217
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/217
Therefore, the GCF of Fractions 278/217,832/217 is 2/217
Least Common Multiple of 217,217 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 217,217 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,217) = 217
common factors(in case of two or more numbers have common factors) = 1
GCF(217,217) x common factors =217 x 1 = 217
LCM(217,217) = ( 217 × 217 ) / 217
LCM(217,217) = 47089 / 217
LCM(217,217) = 217
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FAQs on GCF of Fractions of 278/217, 832/217
1. What is the HCF of 278,832?
The HCF of 278,832 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 278/217, 832/217?
Answer: GCF of Numerators as per given numbers 278/217, 832/217 is
GCF of Numerators i.e. for 278,832 is 2
LCM of denominators i.e. for 217,217 is 217.
Thus, GCF of Fractions is 2/217.Finally, GCF of Fractions for 278/217, 832/217 is 2/217.