GCF of 707/20, 712/458
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 707/20, 712/458 i.e 1/4580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 707/20, 712/458.
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 707/20,712/458?
Given fractions are 707/20,712/458
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 707/20,712/458, numerators are 707,712
Denominators are 20,458
The GCF of 707,712 is 1 .
LCM of 20,458 is 4580.
The greatest common factor of 707/20,712/458 = [GCF of 707,712]/[LCM of 20,458]= 1/4580
Therefore, the GCF of 707/20,712/458 is 1/4580.
To find the highest common factor of 707,712, we have to find the factors of both numbers and list the highest common factor.
The factors of 707 are 1, 7, 101, 707
The factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712
The HCF of 707,712 is 1.
Lets's calculate GCF of 707,712
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 707,712 By Matching Biggest Common Factor Method
Now, list down the factors of 707
:1,7,101,707
Now, list down the factors of 712
:1,2,4,8,89,178,356,712
Greatest Common Factor
We found the factors 707,712 . The biggest common factor number is the GCF number.
So the greatest common factor 707,712 is 1.
Lets's calculate LCM of 20,458
| 2 | 20, 458 |
| 10, 229 |
∴ So the LCM of the given numbers is 2 x 10 x 229 = 4580
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4580
Therefore, the GCF of Fractions 707/20,712/458 is 1/4580
Least Common Multiple of 20,458 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 20,458 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,458) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(20,458) x common factors =2 x 1 = 2
LCM(20,458) = ( 20 × 458 ) / 2
LCM(20,458) = 9160 / 2
LCM(20,458) = 4580
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FAQs on GCF of Fractions of 707/20, 712/458
1. What is the HCF of 707,712?
The HCF of 707,712 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 707/20, 712/458?
Answer: GCF of Numerators as per given numbers 707/20, 712/458 is
GCF of Numerators i.e. for 707,712 is 1
LCM of denominators i.e. for 20,458 is 4580.
Thus, GCF of Fractions is 1/4580.Finally, GCF of Fractions for 707/20, 712/458 is 1/4580.