GCF of 605/42, 714/411
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 605/42, 714/411 i.e 1/5754 easily. The following is the detailed procedure to determine the greatest common factor of fractions 605/42, 714/411.
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 605/42,714/411?
Given fractions are 605/42,714/411
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 605/42,714/411, numerators are 605,714
Denominators are 42,411
The GCF of 605,714 is 1 .
LCM of 42,411 is 5754.
The greatest common factor of 605/42,714/411 = [GCF of 605,714]/[LCM of 42,411]= 1/5754
Therefore, the GCF of 605/42,714/411 is 1/5754.
To find the highest common factor of 605,714, we have to find the factors of both numbers and list the highest common factor.
The factors of 605 are 1, 5, 11, 55, 121, 605
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The HCF of 605,714 is 1.
Lets's calculate GCF of 605,714
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 605,714 By Matching Biggest Common Factor Method
Now, list down the factors of 605
:1,5,11,55,121,605
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Greatest Common Factor
We found the factors 605,714 . The biggest common factor number is the GCF number.
So the greatest common factor 605,714 is 1.
Lets's calculate LCM of 42,411
| 3 | 42, 411 |
| 14, 137 |
∴ So the LCM of the given numbers is 3 x 14 x 137 = 5754
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5754
Therefore, the GCF of Fractions 605/42,714/411 is 1/5754
Least Common Multiple of 42,411 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 42,411 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,411) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(42,411) x common factors =3 x 1 = 3
LCM(42,411) = ( 42 × 411 ) / 3
LCM(42,411) = 17262 / 3
LCM(42,411) = 5754
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FAQs on GCF of Fractions of 605/42, 714/411
1. What is the HCF of 605,714?
The HCF of 605,714 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 605/42, 714/411?
Answer: GCF of Numerators as per given numbers 605/42, 714/411 is
GCF of Numerators i.e. for 605,714 is 1
LCM of denominators i.e. for 42,411 is 5754.
Thus, GCF of Fractions is 1/5754.Finally, GCF of Fractions for 605/42, 714/411 is 1/5754.