GCF of 34/84, 184/89, 364/178
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/84, 184/89, 364/178 i.e 2/7476 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/84, 184/89, 364/178.
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 34/84,184/89,364/178?
Given fractions are 34/84,184/89,364/178
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 34/84,184/89,364/178, numerators are 34,184,364
Denominators are 84,89,178
The GCF of 34,184,364 is 2 .
LCM of 84,89,178 is 7476.
The greatest common factor of 34/84,184/89,364/178 = [GCF of 34,184,364]/[LCM of 84,89,178]= 2/7476
Therefore, the GCF of 34/84,184/89,364/178 is 2/7476.
To find the highest common factor of 34,184,364, 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 184 are 1, 2, 4, 8, 23, 46, 92, 184
The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
The HCF of 34,184,364 is 2.
Lets's calculate GCF of 34,184,364
| 2 | 34, 184, 364 |
| 17, 92, 182 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 34,184,364 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 184
:1,2,4,8,23,46,92,184
Now, list down the factors of 364
:1,2,4,7,13,14,26,28,52,91,182,364
Greatest Common Factor
We found the factors 34,184,364 . The biggest common factor number is the GCF number.
So the greatest common factor 34,184,364 is 2.
Lets's calculate LCM of 84,89,178
| 2 | 84, 89, 178 |
| 89 | 42, 89, 89 |
| 42, 1, 1 |
∴ So the LCM of the given numbers is 2 x 89 x 42 x 1 x 1 = 7476
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7476
Therefore, the GCF of Fractions 34/84,184/89,364/178 is 2/7476
Least Common Multiple of 84,89,178 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 84,89,178 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,89,178) = 1
common factors(in case of two or more numbers have common factors) = 178
GCF(84,89,178) x common factors =1 x 178 = 178
LCM(84,89,178) = ( 84 × 89 × 178 ) / 178
LCM(84,89,178) = 1330728 / 178
LCM(84,89,178) = 7476
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FAQs on GCF of Fractions of 34/84, 184/89, 364/178
1. What is the HCF of 34,184,364?
The HCF of 34,184,364 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 34/84, 184/89, 364/178?
Answer: GCF of Numerators as per given numbers 34/84, 184/89, 364/178 is
GCF of Numerators i.e. for 34,184,364 is 2
LCM of denominators i.e. for 84,89,178 is 7476.
Thus, GCF of Fractions is 2/7476.Finally, GCF of Fractions for 34/84, 184/89, 364/178 is 2/7476.