GCF of 1758/500, 7707/7974
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1758/500, 7707/7974 i.e 3/1993500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1758/500, 7707/7974.
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 1758/500,7707/7974?
Given fractions are 1758/500,7707/7974
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 1758/500,7707/7974, numerators are 1758,7707
Denominators are 500,7974
The GCF of 1758,7707 is 3 .
LCM of 500,7974 is 1993500.
The greatest common factor of 1758/500,7707/7974 = [GCF of 1758,7707]/[LCM of 500,7974]= 3/1993500
Therefore, the GCF of 1758/500,7707/7974 is 3/1993500.
To find the highest common factor of 1758,7707, we have to find the factors of both numbers and list the highest common factor.
The factors of 1758 are 1, 2, 3, 6, 293, 586, 879, 1758
The factors of 7707 are 1, 3, 7, 21, 367, 1101, 2569, 7707
The HCF of 1758,7707 is 3.
Lets's calculate GCF of 1758,7707
| 3 | 1758, 7707 |
| 586, 2569 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1758,7707 By Matching Biggest Common Factor Method
Now, list down the factors of 1758
:1,2,3,6,293,586,879,1758
Now, list down the factors of 7707
:1,3,7,21,367,1101,2569,7707
Greatest Common Factor
We found the factors 1758,7707 . The biggest common factor number is the GCF number.
So the greatest common factor 1758,7707 is 3.
Lets's calculate LCM of 500,7974
| 2 | 500, 7974 |
| 250, 3987 |
∴ So the LCM of the given numbers is 2 x 250 x 3987 = 1993500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1993500
Therefore, the GCF of Fractions 1758/500,7707/7974 is 3/1993500
Least Common Multiple of 500,7974 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 500,7974 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(500,7974) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(500,7974) x common factors =2 x 1 = 2
LCM(500,7974) = ( 500 × 7974 ) / 2
LCM(500,7974) = 3987000 / 2
LCM(500,7974) = 1993500
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FAQs on GCF of Fractions of 1758/500, 7707/7974
1. What is the HCF of 1758,7707?
The HCF of 1758,7707 is 3
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 1758/500, 7707/7974?
Answer: GCF of Numerators as per given numbers 1758/500, 7707/7974 is
GCF of Numerators i.e. for 1758,7707 is 3
LCM of denominators i.e. for 500,7974 is 1993500.
Thus, GCF of Fractions is 3/1993500.Finally, GCF of Fractions for 1758/500, 7707/7974 is 3/1993500.