GCF of 782/71, 713/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 782/71, 713/414 i.e 23/29394 easily. The following is the detailed procedure to determine the greatest common factor of fractions 782/71, 713/414.
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 782/71,713/414?
Given fractions are 782/71,713/414
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 782/71,713/414, numerators are 782,713
Denominators are 71,414
The GCF of 782,713 is 23 .
LCM of 71,414 is 29394.
The greatest common factor of 782/71,713/414 = [GCF of 782,713]/[LCM of 71,414]= 23/29394
Therefore, the GCF of 782/71,713/414 is 23/29394.
To find the highest common factor of 782,713, we have to find the factors of both numbers and list the highest common factor.
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The factors of 713 are 1, 23, 31, 713
The HCF of 782,713 is 23.
Lets's calculate GCF of 782,713
| 23 | 782, 713 |
| 34, 31 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 782,713 By Matching Biggest Common Factor Method
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Now, list down the factors of 713
:1,23,31,713
Greatest Common Factor
We found the factors 782,713 . The biggest common factor number is the GCF number.
So the greatest common factor 782,713 is 23.
Lets's calculate LCM of 71,414
Given numbers has no common factors except 1. So, there LCM is their product i.e 29394
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/29394
Therefore, the GCF of Fractions 782/71,713/414 is 23/29394
Least Common Multiple of 71,414 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 71,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,414) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(71,414) x common factors =1 x 1 = 1
LCM(71,414) = ( 71 × 414 ) / 1
LCM(71,414) = 29394 / 1
LCM(71,414) = 29394
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FAQs on GCF of Fractions of 782/71, 713/414
1. What is the HCF of 782,713?
The HCF of 782,713 is 23
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 782/71, 713/414?
Answer: GCF of Numerators as per given numbers 782/71, 713/414 is
GCF of Numerators i.e. for 782,713 is 23
LCM of denominators i.e. for 71,414 is 29394.
Thus, GCF of Fractions is 23/29394.Finally, GCF of Fractions for 782/71, 713/414 is 23/29394.