GCF of 70/77, 27/320, 698/340
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 70/77, 27/320, 698/340 i.e 1/418880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/77, 27/320, 698/340.
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 70/77,27/320,698/340?
Given fractions are 70/77,27/320,698/340
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 70/77,27/320,698/340, numerators are 70,27,698
Denominators are 77,320,340
The GCF of 70,27,698 is 1 .
LCM of 77,320,340 is 418880.
The greatest common factor of 70/77,27/320,698/340 = [GCF of 70,27,698]/[LCM of 77,320,340]= 1/418880
Therefore, the GCF of 70/77,27/320,698/340 is 1/418880.
To find the highest common factor of 70,27,698, we have to find the factors of both numbers and list the highest common factor.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 27 are 1, 3, 9, 27
The factors of 698 are 1, 2, 349, 698
The HCF of 70,27,698 is 1.
Lets's calculate GCF of 70,27,698
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 70,27,698 By Matching Biggest Common Factor Method
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 698
:1,2,349,698
Greatest Common Factor
We found the factors 70,27,698 . The biggest common factor number is the GCF number.
So the greatest common factor 70,27,698 is 1.
Lets's calculate LCM of 77,320,340
| 2 | 77, 320, 340 |
| 2 | 77, 160, 170 |
| 5 | 77, 80, 85 |
| 77, 16, 17 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 77 x 16 x 17 = 418880
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/418880
Therefore, the GCF of Fractions 70/77,27/320,698/340 is 1/418880
Least Common Multiple of 77,320,340 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 77,320,340 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,320,340) = 1
common factors(in case of two or more numbers have common factors) = 20
GCF(77,320,340) x common factors =1 x 20 = 20
LCM(77,320,340) = ( 77 × 320 × 340 ) / 20
LCM(77,320,340) = 8377600 / 20
LCM(77,320,340) = 418880
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 70/77, 27/320, 698/340
1. What is the HCF of 70,27,698?
The HCF of 70,27,698 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 70/77, 27/320, 698/340?
Answer: GCF of Numerators as per given numbers 70/77, 27/320, 698/340 is
GCF of Numerators i.e. for 70,27,698 is 1
LCM of denominators i.e. for 77,320,340 is 418880.
Thus, GCF of Fractions is 1/418880.Finally, GCF of Fractions for 70/77, 27/320, 698/340 is 1/418880.