GCF of 34/19, 42/68, 312/51
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/19, 42/68, 312/51 i.e 2/3876 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/19, 42/68, 312/51.
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 34/19,42/68,312/51?
Given fractions are 34/19,42/68,312/51
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 34/19,42/68,312/51, numerators are 34,42,312
Denominators are 19,68,51
The GCF of 34,42,312 is 2 .
LCM of 19,68,51 is 3876.
The greatest common factor of 34/19,42/68,312/51 = [GCF of 34,42,312]/[LCM of 19,68,51]= 2/3876
Therefore, the GCF of 34/19,42/68,312/51 is 2/3876.
To find the highest common factor of 34,42,312, 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 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 34,42,312 is 2.
Lets's calculate GCF of 34,42,312
| 2 | 34, 42, 312 |
| 17, 21, 156 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 34,42,312 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 34,42,312 . The biggest common factor number is the GCF number.
So the greatest common factor 34,42,312 is 2.
Lets's calculate LCM of 19,68,51
| 17 | 19, 68, 51 |
| 19, 4, 3 |
∴ So the LCM of the given numbers is 17 x 19 x 4 x 3 = 3876
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3876
Therefore, the GCF of Fractions 34/19,42/68,312/51 is 2/3876
Least Common Multiple of 19,68,51 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 19,68,51 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(19,68,51) = 1
common factors(in case of two or more numbers have common factors) = 17
GCF(19,68,51) x common factors =1 x 17 = 17
LCM(19,68,51) = ( 19 × 68 × 51 ) / 17
LCM(19,68,51) = 65892 / 17
LCM(19,68,51) = 3876
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FAQs on GCF of Fractions of 34/19, 42/68, 312/51
1. What is the HCF of 34,42,312?
The HCF of 34,42,312 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 34/19, 42/68, 312/51?
Answer: GCF of Numerators as per given numbers 34/19, 42/68, 312/51 is
GCF of Numerators i.e. for 34,42,312 is 2
LCM of denominators i.e. for 19,68,51 is 3876.
Thus, GCF of Fractions is 2/3876.Finally, GCF of Fractions for 34/19, 42/68, 312/51 is 2/3876.