GCF of 1991/758, 1680/4598
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1991/758, 1680/4598 i.e 1/1742642 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1991/758, 1680/4598.
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 1991/758,1680/4598?
Given fractions are 1991/758,1680/4598
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 1991/758,1680/4598, numerators are 1991,1680
Denominators are 758,4598
The GCF of 1991,1680 is 1 .
LCM of 758,4598 is 1742642.
The greatest common factor of 1991/758,1680/4598 = [GCF of 1991,1680]/[LCM of 758,4598]= 1/1742642
Therefore, the GCF of 1991/758,1680/4598 is 1/1742642.
To find the highest common factor of 1991,1680, we have to find the factors of both numbers and list the highest common factor.
The factors of 1991 are 1, 11, 181, 1991
The factors of 1680 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680
The HCF of 1991,1680 is 1.
Lets's calculate GCF of 1991,1680
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1991,1680 By Matching Biggest Common Factor Method
Now, list down the factors of 1991
:1,11,181,1991
Now, list down the factors of 1680
:1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30,35,40,42,48,56,60,70,80,84,105,112,120,140,168,210,240,280,336,420,560,840,1680
Greatest Common Factor
We found the factors 1991,1680 . The biggest common factor number is the GCF number.
So the greatest common factor 1991,1680 is 1.
Lets's calculate LCM of 758,4598
| 2 | 758, 4598 |
| 379, 2299 |
∴ So the LCM of the given numbers is 2 x 379 x 2299 = 1742642
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1742642
Therefore, the GCF of Fractions 1991/758,1680/4598 is 1/1742642
Least Common Multiple of 758,4598 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 758,4598 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(758,4598) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(758,4598) x common factors =2 x 1 = 2
LCM(758,4598) = ( 758 × 4598 ) / 2
LCM(758,4598) = 3485284 / 2
LCM(758,4598) = 1742642
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FAQs on GCF of Fractions of 1991/758, 1680/4598
1. What is the HCF of 1991,1680?
The HCF of 1991,1680 is 1
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 1991/758, 1680/4598?
Answer: GCF of Numerators as per given numbers 1991/758, 1680/4598 is
GCF of Numerators i.e. for 1991,1680 is 1
LCM of denominators i.e. for 758,4598 is 1742642.
Thus, GCF of Fractions is 1/1742642.Finally, GCF of Fractions for 1991/758, 1680/4598 is 1/1742642.