GCF of 42/21, 691/48, 814/106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 42/21, 691/48, 814/106 i.e 1/17808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/21, 691/48, 814/106.
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 42/21,691/48,814/106?
Given fractions are 42/21,691/48,814/106
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 42/21,691/48,814/106, numerators are 42,691,814
Denominators are 21,48,106
The GCF of 42,691,814 is 1 .
LCM of 21,48,106 is 17808.
The greatest common factor of 42/21,691/48,814/106 = [GCF of 42,691,814]/[LCM of 21,48,106]= 1/17808
Therefore, the GCF of 42/21,691/48,814/106 is 1/17808.
To find the highest common factor of 42,691,814, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 691 are 1, 691
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The HCF of 42,691,814 is 1.
Lets's calculate GCF of 42,691,814
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 42,691,814 By Matching Biggest Common Factor Method
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 691
:1,691
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Greatest Common Factor
We found the factors 42,691,814 . The biggest common factor number is the GCF number.
So the greatest common factor 42,691,814 is 1.
Lets's calculate LCM of 21,48,106
| 2 | 21, 48, 106 |
| 3 | 21, 24, 53 |
| 7, 8, 53 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 8 x 53 = 17808
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17808
Therefore, the GCF of Fractions 42/21,691/48,814/106 is 1/17808
Least Common Multiple of 21,48,106 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 21,48,106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,48,106) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(21,48,106) x common factors =1 x 6 = 6
LCM(21,48,106) = ( 21 × 48 × 106 ) / 6
LCM(21,48,106) = 106848 / 6
LCM(21,48,106) = 17808
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FAQs on GCF of Fractions of 42/21, 691/48, 814/106
1. What is the HCF of 42,691,814?
The HCF of 42,691,814 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 42/21, 691/48, 814/106?
Answer: GCF of Numerators as per given numbers 42/21, 691/48, 814/106 is
GCF of Numerators i.e. for 42,691,814 is 1
LCM of denominators i.e. for 21,48,106 is 17808.
Thus, GCF of Fractions is 1/17808.Finally, GCF of Fractions for 42/21, 691/48, 814/106 is 1/17808.