GCF of 177/658, 192/274
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 177/658, 192/274 i.e 3/90146 easily. The following is the detailed procedure to determine the greatest common factor of fractions 177/658, 192/274.
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 177/658,192/274?
Given fractions are 177/658,192/274
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 177/658,192/274, numerators are 177,192
Denominators are 658,274
The GCF of 177,192 is 3 .
LCM of 658,274 is 90146.
The greatest common factor of 177/658,192/274 = [GCF of 177,192]/[LCM of 658,274]= 3/90146
Therefore, the GCF of 177/658,192/274 is 3/90146.
To find the highest common factor of 177,192, we have to find the factors of both numbers and list the highest common factor.
The factors of 177 are 1, 3, 59, 177
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
The HCF of 177,192 is 3.
Lets's calculate GCF of 177,192
| 3 | 177, 192 |
| 59, 64 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 177,192 By Matching Biggest Common Factor Method
Now, list down the factors of 177
:1,3,59,177
Now, list down the factors of 192
:1,2,3,4,6,8,12,16,24,32,48,64,96,192
Greatest Common Factor
We found the factors 177,192 . The biggest common factor number is the GCF number.
So the greatest common factor 177,192 is 3.
Lets's calculate LCM of 658,274
| 2 | 658, 274 |
| 329, 137 |
∴ So the LCM of the given numbers is 2 x 329 x 137 = 90146
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/90146
Therefore, the GCF of Fractions 177/658,192/274 is 3/90146
Least Common Multiple of 658,274 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 658,274 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(658,274) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(658,274) x common factors =2 x 1 = 2
LCM(658,274) = ( 658 × 274 ) / 2
LCM(658,274) = 180292 / 2
LCM(658,274) = 90146
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FAQs on GCF of Fractions of 177/658, 192/274
1. What is the HCF of 177,192?
The HCF of 177,192 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 177/658, 192/274?
Answer: GCF of Numerators as per given numbers 177/658, 192/274 is
GCF of Numerators i.e. for 177,192 is 3
LCM of denominators i.e. for 658,274 is 90146.
Thus, GCF of Fractions is 3/90146.Finally, GCF of Fractions for 177/658, 192/274 is 3/90146.