GCF of 832/998, 312/666
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 832/998, 312/666 i.e 104/332334 easily. The following is the detailed procedure to determine the greatest common factor of fractions 832/998, 312/666.
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 832/998,312/666?
Given fractions are 832/998,312/666
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 832/998,312/666, numerators are 832,312
Denominators are 998,666
The GCF of 832,312 is 104 .
LCM of 998,666 is 332334.
The greatest common factor of 832/998,312/666 = [GCF of 832,312]/[LCM of 998,666]= 104/332334
Therefore, the GCF of 832/998,312/666 is 104/332334.
To find the highest common factor of 832,312, 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 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 832,312 is 104.
Lets's calculate GCF of 832,312
| 2 | 832, 312 |
| 2 | 416, 156 |
| 2 | 208, 78 |
| 13 | 104, 39 |
| 8, 3 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 13 = 104
Greatest Common Factor of 832,312 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 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 832,312 . The biggest common factor number is the GCF number.
So the greatest common factor 832,312 is 104.
Lets's calculate LCM of 998,666
| 2 | 998, 666 |
| 499, 333 |
∴ So the LCM of the given numbers is 2 x 499 x 333 = 332334
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 104/332334
Therefore, the GCF of Fractions 832/998,312/666 is 104/332334
Least Common Multiple of 998,666 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 998,666 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(998,666) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(998,666) x common factors =2 x 1 = 2
LCM(998,666) = ( 998 × 666 ) / 2
LCM(998,666) = 664668 / 2
LCM(998,666) = 332334
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FAQs on GCF of Fractions of 832/998, 312/666
1. What is the HCF of 832,312?
The HCF of 832,312 is 104
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 832/998, 312/666?
Answer: GCF of Numerators as per given numbers 832/998, 312/666 is
GCF of Numerators i.e. for 832,312 is 104
LCM of denominators i.e. for 998,666 is 332334.
Thus, GCF of Fractions is 104/332334.Finally, GCF of Fractions for 832/998, 312/666 is 104/332334.