GCF of 34/12, 96/46, 67/23, 42/206
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/12, 96/46, 67/23, 42/206 i.e 1/28428 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/12, 96/46, 67/23, 42/206.
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 34/12,96/46,67/23,42/206?
Given fractions are 34/12,96/46,67/23,42/206
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 34/12,96/46,67/23,42/206, numerators are 34,96,67,42
Denominators are 12,46,23,206
The GCF of 34,96,67,42 is 1 .
LCM of 12,46,23,206 is 28428.
The greatest common factor of 34/12,96/46,67/23,42/206 = [GCF of 34,96,67,42]/[LCM of 12,46,23,206]= 1/28428
Therefore, the GCF of 34/12,96/46,67/23,42/206 is 1/28428.
To find the highest common factor of 34,96,67,42, 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 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 67 are 1, 67
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The HCF of 34,96,67,42 is 1.
Lets's calculate GCF of 34,96,67,42
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 34,96,67,42 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 67
:1,67
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Greatest Common Factor
We found the factors 34,96,67,42 . The biggest common factor number is the GCF number.
So the greatest common factor 34,96,67,42 is 1.
Lets's calculate LCM of 12,46,23,206
| 2 | 12, 46, 23, 206 |
| 23 | 6, 23, 23, 103 |
| 6, 1, 1, 103 |
∴ So the LCM of the given numbers is 2 x 23 x 6 x 1 x 1 x 103 = 28428
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28428
Therefore, the GCF of Fractions 34/12,96/46,67/23,42/206 is 1/28428
Least Common Multiple of 12,46,23,206 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 12,46,23,206 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,46,23,206) = 1
common factors(in case of two or more numbers have common factors) = 92
GCF(12,46,23,206) x common factors =1 x 92 = 92
LCM(12,46,23,206) = ( 12 × 46 × 23 × 206 ) / 92
LCM(12,46,23,206) = 2615376 / 92
LCM(12,46,23,206) = 28428
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 34/12, 96/46, 67/23, 42/206
1. What is the HCF of 34,96,67,42?
The HCF of 34,96,67,42 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 34/12, 96/46, 67/23, 42/206?
Answer: GCF of Numerators as per given numbers 34/12, 96/46, 67/23, 42/206 is
GCF of Numerators i.e. for 34,96,67,42 is 1
LCM of denominators i.e. for 12,46,23,206 is 28428.
Thus, GCF of Fractions is 1/28428.Finally, GCF of Fractions for 34/12, 96/46, 67/23, 42/206 is 1/28428.