GCF of 6973/178, 2314/222
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6973/178, 2314/222 i.e 1/19758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6973/178, 2314/222.
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 6973/178,2314/222?
Given fractions are 6973/178,2314/222
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 6973/178,2314/222, numerators are 6973,2314
Denominators are 178,222
The GCF of 6973,2314 is 1 .
LCM of 178,222 is 19758.
The greatest common factor of 6973/178,2314/222 = [GCF of 6973,2314]/[LCM of 178,222]= 1/19758
Therefore, the GCF of 6973/178,2314/222 is 1/19758.
To find the highest common factor of 6973,2314, we have to find the factors of both numbers and list the highest common factor.
The factors of 6973 are 1, 19, 367, 6973
The factors of 2314 are 1, 2, 13, 26, 89, 178, 1157, 2314
The HCF of 6973,2314 is 1.
Lets's calculate GCF of 6973,2314
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 6973,2314 By Matching Biggest Common Factor Method
Now, list down the factors of 6973
:1,19,367,6973
Now, list down the factors of 2314
:1,2,13,26,89,178,1157,2314
Greatest Common Factor
We found the factors 6973,2314 . The biggest common factor number is the GCF number.
So the greatest common factor 6973,2314 is 1.
Lets's calculate LCM of 178,222
| 2 | 178, 222 |
| 89, 111 |
∴ So the LCM of the given numbers is 2 x 89 x 111 = 19758
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/19758
Therefore, the GCF of Fractions 6973/178,2314/222 is 1/19758
Least Common Multiple of 178,222 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 178,222 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(178,222) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(178,222) x common factors =2 x 1 = 2
LCM(178,222) = ( 178 × 222 ) / 2
LCM(178,222) = 39516 / 2
LCM(178,222) = 19758
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FAQs on GCF of Fractions of 6973/178, 2314/222
1. What is the HCF of 6973,2314?
The HCF of 6973,2314 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 6973/178, 2314/222?
Answer: GCF of Numerators as per given numbers 6973/178, 2314/222 is
GCF of Numerators i.e. for 6973,2314 is 1
LCM of denominators i.e. for 178,222 is 19758.
Thus, GCF of Fractions is 1/19758.Finally, GCF of Fractions for 6973/178, 2314/222 is 1/19758.