GCF of 34/18, 84/15, 906/986
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/18, 84/15, 906/986 i.e 2/44370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/18, 84/15, 906/986.
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 34/18,84/15,906/986?
Given fractions are 34/18,84/15,906/986
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 34/18,84/15,906/986, numerators are 34,84,906
Denominators are 18,15,986
The GCF of 34,84,906 is 2 .
LCM of 18,15,986 is 44370.
The greatest common factor of 34/18,84/15,906/986 = [GCF of 34,84,906]/[LCM of 18,15,986]= 2/44370
Therefore, the GCF of 34/18,84/15,906/986 is 2/44370.
To find the highest common factor of 34,84,906, 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 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 906 are 1, 2, 3, 6, 151, 302, 453, 906
The HCF of 34,84,906 is 2.
Lets's calculate GCF of 34,84,906
| 2 | 34, 84, 906 |
| 17, 42, 453 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 34,84,906 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 906
:1,2,3,6,151,302,453,906
Greatest Common Factor
We found the factors 34,84,906 . The biggest common factor number is the GCF number.
So the greatest common factor 34,84,906 is 2.
Lets's calculate LCM of 18,15,986
| 2 | 18, 15, 986 |
| 3 | 9, 15, 493 |
| 3, 5, 493 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 493 = 44370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/44370
Therefore, the GCF of Fractions 34/18,84/15,906/986 is 2/44370
Least Common Multiple of 18,15,986 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 18,15,986 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(18,15,986) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(18,15,986) x common factors =1 x 6 = 6
LCM(18,15,986) = ( 18 × 15 × 986 ) / 6
LCM(18,15,986) = 266220 / 6
LCM(18,15,986) = 44370
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 34/18, 84/15, 906/986
1. What is the HCF of 34,84,906?
The HCF of 34,84,906 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 34/18, 84/15, 906/986?
Answer: GCF of Numerators as per given numbers 34/18, 84/15, 906/986 is
GCF of Numerators i.e. for 34,84,906 is 2
LCM of denominators i.e. for 18,15,986 is 44370.
Thus, GCF of Fractions is 2/44370.Finally, GCF of Fractions for 34/18, 84/15, 906/986 is 2/44370.