GCF of 705/364, 164/105, 335/342
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 705/364, 164/105, 335/342 i.e 1/311220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 705/364, 164/105, 335/342.
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 705/364,164/105,335/342?
Given fractions are 705/364,164/105,335/342
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 705/364,164/105,335/342, numerators are 705,164,335
Denominators are 364,105,342
The GCF of 705,164,335 is 1 .
LCM of 364,105,342 is 311220.
The greatest common factor of 705/364,164/105,335/342 = [GCF of 705,164,335]/[LCM of 364,105,342]= 1/311220
Therefore, the GCF of 705/364,164/105,335/342 is 1/311220.
To find the highest common factor of 705,164,335, we have to find the factors of both numbers and list the highest common factor.
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The factors of 164 are 1, 2, 4, 41, 82, 164
The factors of 335 are 1, 5, 67, 335
The HCF of 705,164,335 is 1.
Lets's calculate GCF of 705,164,335
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 705,164,335 By Matching Biggest Common Factor Method
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Now, list down the factors of 164
:1,2,4,41,82,164
Now, list down the factors of 335
:1,5,67,335
Greatest Common Factor
We found the factors 705,164,335 . The biggest common factor number is the GCF number.
So the greatest common factor 705,164,335 is 1.
Lets's calculate LCM of 364,105,342
| 2 | 364, 105, 342 |
| 3 | 182, 105, 171 |
| 7 | 182, 35, 57 |
| 26, 5, 57 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 26 x 5 x 57 = 311220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/311220
Therefore, the GCF of Fractions 705/364,164/105,335/342 is 1/311220
Least Common Multiple of 364,105,342 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 364,105,342 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(364,105,342) = 1
common factors(in case of two or more numbers have common factors) = 42
GCF(364,105,342) x common factors =1 x 42 = 42
LCM(364,105,342) = ( 364 × 105 × 342 ) / 42
LCM(364,105,342) = 13071240 / 42
LCM(364,105,342) = 311220
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FAQs on GCF of Fractions of 705/364, 164/105, 335/342
1. What is the HCF of 705,164,335?
The HCF of 705,164,335 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 705/364, 164/105, 335/342?
Answer: GCF of Numerators as per given numbers 705/364, 164/105, 335/342 is
GCF of Numerators i.e. for 705,164,335 is 1
LCM of denominators i.e. for 364,105,342 is 311220.
Thus, GCF of Fractions is 1/311220.Finally, GCF of Fractions for 705/364, 164/105, 335/342 is 1/311220.