GCF of 321/693, 114/174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 321/693, 114/174 i.e 3/40194 easily. The following is the detailed procedure to determine the greatest common factor of fractions 321/693, 114/174.
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 321/693,114/174?
Given fractions are 321/693,114/174
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 321/693,114/174, numerators are 321,114
Denominators are 693,174
The GCF of 321,114 is 3 .
LCM of 693,174 is 40194.
The greatest common factor of 321/693,114/174 = [GCF of 321,114]/[LCM of 693,174]= 3/40194
Therefore, the GCF of 321/693,114/174 is 3/40194.
To find the highest common factor of 321,114, we have to find the factors of both numbers and list the highest common factor.
The factors of 321 are 1, 3, 107, 321
The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114
The HCF of 321,114 is 3.
Lets's calculate GCF of 321,114
| 3 | 321, 114 |
| 107, 38 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 321,114 By Matching Biggest Common Factor Method
Now, list down the factors of 321
:1,3,107,321
Now, list down the factors of 114
:1,2,3,6,19,38,57,114
Greatest Common Factor
We found the factors 321,114 . The biggest common factor number is the GCF number.
So the greatest common factor 321,114 is 3.
Lets's calculate LCM of 693,174
| 3 | 693, 174 |
| 231, 58 |
∴ So the LCM of the given numbers is 3 x 231 x 58 = 40194
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/40194
Therefore, the GCF of Fractions 321/693,114/174 is 3/40194
Least Common Multiple of 693,174 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 693,174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(693,174) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(693,174) x common factors =3 x 1 = 3
LCM(693,174) = ( 693 × 174 ) / 3
LCM(693,174) = 120582 / 3
LCM(693,174) = 40194
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FAQs on GCF of Fractions of 321/693, 114/174
1. What is the HCF of 321,114?
The HCF of 321,114 is 3
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 321/693, 114/174?
Answer: GCF of Numerators as per given numbers 321/693, 114/174 is
GCF of Numerators i.e. for 321,114 is 3
LCM of denominators i.e. for 693,174 is 40194.
Thus, GCF of Fractions is 3/40194.Finally, GCF of Fractions for 321/693, 114/174 is 3/40194.