GCF of 712/341, 524/105
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 712/341, 524/105 i.e 4/35805 easily. The following is the detailed procedure to determine the greatest common factor of fractions 712/341, 524/105.
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 712/341,524/105?
Given fractions are 712/341,524/105
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 712/341,524/105, numerators are 712,524
Denominators are 341,105
The GCF of 712,524 is 4 .
LCM of 341,105 is 35805.
The greatest common factor of 712/341,524/105 = [GCF of 712,524]/[LCM of 341,105]= 4/35805
Therefore, the GCF of 712/341,524/105 is 4/35805.
To find the highest common factor of 712,524, we have to find the factors of both numbers and list the highest common factor.
The factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712
The factors of 524 are 1, 2, 4, 131, 262, 524
The HCF of 712,524 is 4.
Lets's calculate GCF of 712,524
| 2 | 712, 524 |
| 2 | 356, 262 |
| 178, 131 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 712,524 By Matching Biggest Common Factor Method
Now, list down the factors of 712
:1,2,4,8,89,178,356,712
Now, list down the factors of 524
:1,2,4,131,262,524
Greatest Common Factor
We found the factors 712,524 . The biggest common factor number is the GCF number.
So the greatest common factor 712,524 is 4.
Lets's calculate LCM of 341,105
Given numbers has no common factors except 1. So, there LCM is their product i.e 35805
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/35805
Therefore, the GCF of Fractions 712/341,524/105 is 4/35805
Least Common Multiple of 341,105 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 341,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(341,105) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(341,105) x common factors =1 x 1 = 1
LCM(341,105) = ( 341 × 105 ) / 1
LCM(341,105) = 35805 / 1
LCM(341,105) = 35805
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FAQs on GCF of Fractions of 712/341, 524/105
1. What is the HCF of 712,524?
The HCF of 712,524 is 4
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 712/341, 524/105?
Answer: GCF of Numerators as per given numbers 712/341, 524/105 is
GCF of Numerators i.e. for 712,524 is 4
LCM of denominators i.e. for 341,105 is 35805.
Thus, GCF of Fractions is 4/35805.Finally, GCF of Fractions for 712/341, 524/105 is 4/35805.