GCF of 783/80, 705/769
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 783/80, 705/769 i.e 3/61520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 783/80, 705/769.
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 783/80,705/769?
Given fractions are 783/80,705/769
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 783/80,705/769, numerators are 783,705
Denominators are 80,769
The GCF of 783,705 is 3 .
LCM of 80,769 is 61520.
The greatest common factor of 783/80,705/769 = [GCF of 783,705]/[LCM of 80,769]= 3/61520
Therefore, the GCF of 783/80,705/769 is 3/61520.
To find the highest common factor of 783,705, we have to find the factors of both numbers and list the highest common factor.
The factors of 783 are 1, 3, 9, 27, 29, 87, 261, 783
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The HCF of 783,705 is 3.
Lets's calculate GCF of 783,705
| 3 | 783, 705 |
| 261, 235 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 783,705 By Matching Biggest Common Factor Method
Now, list down the factors of 783
:1,3,9,27,29,87,261,783
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 783,705 . The biggest common factor number is the GCF number.
So the greatest common factor 783,705 is 3.
Lets's calculate LCM of 80,769
Given numbers has no common factors except 1. So, there LCM is their product i.e 61520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/61520
Therefore, the GCF of Fractions 783/80,705/769 is 3/61520
Least Common Multiple of 80,769 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 80,769 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(80,769) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(80,769) x common factors =1 x 1 = 1
LCM(80,769) = ( 80 × 769 ) / 1
LCM(80,769) = 61520 / 1
LCM(80,769) = 61520
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FAQs on GCF of Fractions of 783/80, 705/769
1. What is the HCF of 783,705?
The HCF of 783,705 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 783/80, 705/769?
Answer: GCF of Numerators as per given numbers 783/80, 705/769 is
GCF of Numerators i.e. for 783,705 is 3
LCM of denominators i.e. for 80,769 is 61520.
Thus, GCF of Fractions is 3/61520.Finally, GCF of Fractions for 783/80, 705/769 is 3/61520.