GCF of 837/31, 225/672
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 837/31, 225/672 i.e 9/20832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 837/31, 225/672.
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 837/31,225/672?
Given fractions are 837/31,225/672
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 837/31,225/672, numerators are 837,225
Denominators are 31,672
The GCF of 837,225 is 9 .
LCM of 31,672 is 20832.
The greatest common factor of 837/31,225/672 = [GCF of 837,225]/[LCM of 31,672]= 9/20832
Therefore, the GCF of 837/31,225/672 is 9/20832.
To find the highest common factor of 837,225, we have to find the factors of both numbers and list the highest common factor.
The factors of 837 are 1, 3, 9, 27, 31, 93, 279, 837
The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225
The HCF of 837,225 is 9.
Lets's calculate GCF of 837,225
| 3 | 837, 225 |
| 3 | 279, 75 |
| 93, 25 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 837,225 By Matching Biggest Common Factor Method
Now, list down the factors of 837
:1,3,9,27,31,93,279,837
Now, list down the factors of 225
:1,3,5,9,15,25,45,75,225
Greatest Common Factor
We found the factors 837,225 . The biggest common factor number is the GCF number.
So the greatest common factor 837,225 is 9.
Lets's calculate LCM of 31,672
Given numbers has no common factors except 1. So, there LCM is their product i.e 20832
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/20832
Therefore, the GCF of Fractions 837/31,225/672 is 9/20832
Least Common Multiple of 31,672 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 31,672 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,672) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,672) x common factors =1 x 1 = 1
LCM(31,672) = ( 31 × 672 ) / 1
LCM(31,672) = 20832 / 1
LCM(31,672) = 20832
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FAQs on GCF of Fractions of 837/31, 225/672
1. What is the HCF of 837,225?
The HCF of 837,225 is 9
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 837/31, 225/672?
Answer: GCF of Numerators as per given numbers 837/31, 225/672 is
GCF of Numerators i.e. for 837,225 is 9
LCM of denominators i.e. for 31,672 is 20832.
Thus, GCF of Fractions is 9/20832.Finally, GCF of Fractions for 837/31, 225/672 is 9/20832.