GCF of 677/164, 6142/290
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 677/164, 6142/290 i.e 1/23780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 677/164, 6142/290.
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 677/164,6142/290?
Given fractions are 677/164,6142/290
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 677/164,6142/290, numerators are 677,6142
Denominators are 164,290
The GCF of 677,6142 is 1 .
LCM of 164,290 is 23780.
The greatest common factor of 677/164,6142/290 = [GCF of 677,6142]/[LCM of 164,290]= 1/23780
Therefore, the GCF of 677/164,6142/290 is 1/23780.
To find the highest common factor of 677,6142, we have to find the factors of both numbers and list the highest common factor.
The factors of 677 are 1, 677
The factors of 6142 are 1, 2, 37, 74, 83, 166, 3071, 6142
The HCF of 677,6142 is 1.
Lets's calculate GCF of 677,6142
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 677,6142 By Matching Biggest Common Factor Method
Now, list down the factors of 677
:1,677
Now, list down the factors of 6142
:1,2,37,74,83,166,3071,6142
Greatest Common Factor
We found the factors 677,6142 . The biggest common factor number is the GCF number.
So the greatest common factor 677,6142 is 1.
Lets's calculate LCM of 164,290
| 2 | 164, 290 |
| 82, 145 |
∴ So the LCM of the given numbers is 2 x 82 x 145 = 23780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23780
Therefore, the GCF of Fractions 677/164,6142/290 is 1/23780
Least Common Multiple of 164,290 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 164,290 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,290) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(164,290) x common factors =2 x 1 = 2
LCM(164,290) = ( 164 × 290 ) / 2
LCM(164,290) = 47560 / 2
LCM(164,290) = 23780
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 677/164, 6142/290
1. What is the HCF of 677,6142?
The HCF of 677,6142 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 677/164, 6142/290?
Answer: GCF of Numerators as per given numbers 677/164, 6142/290 is
GCF of Numerators i.e. for 677,6142 is 1
LCM of denominators i.e. for 164,290 is 23780.
Thus, GCF of Fractions is 1/23780.Finally, GCF of Fractions for 677/164, 6142/290 is 1/23780.