GCF of 1891/488, 9672/5762
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1891/488, 9672/5762 i.e 31/1405928 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1891/488, 9672/5762.
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 1891/488,9672/5762?
Given fractions are 1891/488,9672/5762
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 1891/488,9672/5762, numerators are 1891,9672
Denominators are 488,5762
The GCF of 1891,9672 is 31 .
LCM of 488,5762 is 1405928.
The greatest common factor of 1891/488,9672/5762 = [GCF of 1891,9672]/[LCM of 488,5762]= 31/1405928
Therefore, the GCF of 1891/488,9672/5762 is 31/1405928.
To find the highest common factor of 1891,9672, we have to find the factors of both numbers and list the highest common factor.
The factors of 1891 are 1, 31, 61, 1891
The factors of 9672 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 31, 39, 52, 62, 78, 93, 104, 124, 156, 186, 248, 312, 372, 403, 744, 806, 1209, 1612, 2418, 3224, 4836, 9672
The HCF of 1891,9672 is 31.
Lets's calculate GCF of 1891,9672
| 31 | 1891, 9672 |
| 61, 312 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 1891,9672 By Matching Biggest Common Factor Method
Now, list down the factors of 1891
:1,31,61,1891
Now, list down the factors of 9672
:1,2,3,4,6,8,12,13,24,26,31,39,52,62,78,93,104,124,156,186,248,312,372,403,744,806,1209,1612,2418,3224,4836,9672
Greatest Common Factor
We found the factors 1891,9672 . The biggest common factor number is the GCF number.
So the greatest common factor 1891,9672 is 31.
Lets's calculate LCM of 488,5762
| 2 | 488, 5762 |
| 244, 2881 |
∴ So the LCM of the given numbers is 2 x 244 x 2881 = 1405928
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/1405928
Therefore, the GCF of Fractions 1891/488,9672/5762 is 31/1405928
Least Common Multiple of 488,5762 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 488,5762 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(488,5762) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(488,5762) x common factors =2 x 1 = 2
LCM(488,5762) = ( 488 × 5762 ) / 2
LCM(488,5762) = 2811856 / 2
LCM(488,5762) = 1405928
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FAQs on GCF of Fractions of 1891/488, 9672/5762
1. What is the HCF of 1891,9672?
The HCF of 1891,9672 is 31
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 1891/488, 9672/5762?
Answer: GCF of Numerators as per given numbers 1891/488, 9672/5762 is
GCF of Numerators i.e. for 1891,9672 is 31
LCM of denominators i.e. for 488,5762 is 1405928.
Thus, GCF of Fractions is 31/1405928.Finally, GCF of Fractions for 1891/488, 9672/5762 is 31/1405928.