GCF of 750/770, 830/509
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 750/770, 830/509 i.e 10/391930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 750/770, 830/509.
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 750/770,830/509?
Given fractions are 750/770,830/509
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 750/770,830/509, numerators are 750,830
Denominators are 770,509
The GCF of 750,830 is 10 .
LCM of 770,509 is 391930.
The greatest common factor of 750/770,830/509 = [GCF of 750,830]/[LCM of 770,509]= 10/391930
Therefore, the GCF of 750/770,830/509 is 10/391930.
To find the highest common factor of 750,830, we have to find the factors of both numbers and list the highest common factor.
The factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750
The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830
The HCF of 750,830 is 10.
Lets's calculate GCF of 750,830
| 2 | 750, 830 |
| 5 | 375, 415 |
| 75, 83 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 750,830 By Matching Biggest Common Factor Method
Now, list down the factors of 750
:1,2,3,5,6,10,15,25,30,50,75,125,150,250,375,750
Now, list down the factors of 830
:1,2,5,10,83,166,415,830
Greatest Common Factor
We found the factors 750,830 . The biggest common factor number is the GCF number.
So the greatest common factor 750,830 is 10.
Lets's calculate LCM of 770,509
Given numbers has no common factors except 1. So, there LCM is their product i.e 391930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/391930
Therefore, the GCF of Fractions 750/770,830/509 is 10/391930
Least Common Multiple of 770,509 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 770,509 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(770,509) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(770,509) x common factors =1 x 1 = 1
LCM(770,509) = ( 770 × 509 ) / 1
LCM(770,509) = 391930 / 1
LCM(770,509) = 391930
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FAQs on GCF of Fractions of 750/770, 830/509
1. What is the HCF of 750,830?
The HCF of 750,830 is 10
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 750/770, 830/509?
Answer: GCF of Numerators as per given numbers 750/770, 830/509 is
GCF of Numerators i.e. for 750,830 is 10
LCM of denominators i.e. for 770,509 is 391930.
Thus, GCF of Fractions is 10/391930.Finally, GCF of Fractions for 750/770, 830/509 is 10/391930.