GCF of 832/419, 2912/141
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 832/419, 2912/141 i.e 416/59079 easily. The following is the detailed procedure to determine the greatest common factor of fractions 832/419, 2912/141.
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 832/419,2912/141?
Given fractions are 832/419,2912/141
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 832/419,2912/141, numerators are 832,2912
Denominators are 419,141
The GCF of 832,2912 is 416 .
LCM of 419,141 is 59079.
The greatest common factor of 832/419,2912/141 = [GCF of 832,2912]/[LCM of 419,141]= 416/59079
Therefore, the GCF of 832/419,2912/141 is 416/59079.
To find the highest common factor of 832,2912, we have to find the factors of both numbers and list the highest common factor.
The factors of 832 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832
The factors of 2912 are 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 91, 104, 112, 182, 208, 224, 364, 416, 728, 1456, 2912
The HCF of 832,2912 is 416.
Lets's calculate GCF of 832,2912
| 2 | 832, 2912 |
| 2 | 416, 1456 |
| 2 | 208, 728 |
| 2 | 104, 364 |
| 2 | 52, 182 |
| 13 | 26, 91 |
| 2, 7 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 13 = 416
Greatest Common Factor of 832,2912 By Matching Biggest Common Factor Method
Now, list down the factors of 832
:1,2,4,8,13,16,26,32,52,64,104,208,416,832
Now, list down the factors of 2912
:1,2,4,7,8,13,14,16,26,28,32,52,56,91,104,112,182,208,224,364,416,728,1456,2912
Greatest Common Factor
We found the factors 832,2912 . The biggest common factor number is the GCF number.
So the greatest common factor 832,2912 is 416.
Lets's calculate LCM of 419,141
Given numbers has no common factors except 1. So, there LCM is their product i.e 59079
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 416/59079
Therefore, the GCF of Fractions 832/419,2912/141 is 416/59079
Least Common Multiple of 419,141 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 419,141 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(419,141) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(419,141) x common factors =1 x 1 = 1
LCM(419,141) = ( 419 × 141 ) / 1
LCM(419,141) = 59079 / 1
LCM(419,141) = 59079
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FAQs on GCF of Fractions of 832/419, 2912/141
1. What is the HCF of 832,2912?
The HCF of 832,2912 is 416
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 832/419, 2912/141?
Answer: GCF of Numerators as per given numbers 832/419, 2912/141 is
GCF of Numerators i.e. for 832,2912 is 416
LCM of denominators i.e. for 419,141 is 59079.
Thus, GCF of Fractions is 416/59079.Finally, GCF of Fractions for 832/419, 2912/141 is 416/59079.