GCF of 34/106, 678/817, 134/437
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/106, 678/817, 134/437 i.e 2/1991846 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/106, 678/817, 134/437.
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 34/106,678/817,134/437?
Given fractions are 34/106,678/817,134/437
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 34/106,678/817,134/437, numerators are 34,678,134
Denominators are 106,817,437
The GCF of 34,678,134 is 2 .
LCM of 106,817,437 is 1991846.
The greatest common factor of 34/106,678/817,134/437 = [GCF of 34,678,134]/[LCM of 106,817,437]= 2/1991846
Therefore, the GCF of 34/106,678/817,134/437 is 2/1991846.
To find the highest common factor of 34,678,134, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The factors of 134 are 1, 2, 67, 134
The HCF of 34,678,134 is 2.
Lets's calculate GCF of 34,678,134
| 2 | 34, 678, 134 |
| 17, 339, 67 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 34,678,134 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Now, list down the factors of 134
:1,2,67,134
Greatest Common Factor
We found the factors 34,678,134 . The biggest common factor number is the GCF number.
So the greatest common factor 34,678,134 is 2.
Lets's calculate LCM of 106,817,437
| 19 | 106, 817, 437 |
| 106, 43, 23 |
∴ So the LCM of the given numbers is 19 x 106 x 43 x 23 = 1991846
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1991846
Therefore, the GCF of Fractions 34/106,678/817,134/437 is 2/1991846
Least Common Multiple of 106,817,437 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 106,817,437 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(106,817,437) = 1
common factors(in case of two or more numbers have common factors) = 19
GCF(106,817,437) x common factors =1 x 19 = 19
LCM(106,817,437) = ( 106 × 817 × 437 ) / 19
LCM(106,817,437) = 37845074 / 19
LCM(106,817,437) = 1991846
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FAQs on GCF of Fractions of 34/106, 678/817, 134/437
1. What is the HCF of 34,678,134?
The HCF of 34,678,134 is 2
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 34/106, 678/817, 134/437?
Answer: GCF of Numerators as per given numbers 34/106, 678/817, 134/437 is
GCF of Numerators i.e. for 34,678,134 is 2
LCM of denominators i.e. for 106,817,437 is 1991846.
Thus, GCF of Fractions is 2/1991846.Finally, GCF of Fractions for 34/106, 678/817, 134/437 is 2/1991846.