GCF of 77/98, 80/84, 690/105
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 77/98, 80/84, 690/105 i.e 1/2940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/98, 80/84, 690/105.
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 77/98,80/84,690/105?
Given fractions are 77/98,80/84,690/105
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 77/98,80/84,690/105, numerators are 77,80,690
Denominators are 98,84,105
The GCF of 77,80,690 is 1 .
LCM of 98,84,105 is 2940.
The greatest common factor of 77/98,80/84,690/105 = [GCF of 77,80,690]/[LCM of 98,84,105]= 1/2940
Therefore, the GCF of 77/98,80/84,690/105 is 1/2940.
To find the highest common factor of 77,80,690, we have to find the factors of both numbers and list the highest common factor.
The factors of 77 are 1, 7, 11, 77
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
The HCF of 77,80,690 is 1.
Lets's calculate GCF of 77,80,690
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 77,80,690 By Matching Biggest Common Factor Method
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 690
:1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690
Greatest Common Factor
We found the factors 77,80,690 . The biggest common factor number is the GCF number.
So the greatest common factor 77,80,690 is 1.
Lets's calculate LCM of 98,84,105
| 2 | 98, 84, 105 |
| 3 | 49, 42, 105 |
| 7 | 49, 14, 35 |
| 7, 2, 5 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 7 x 2 x 5 = 2940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2940
Therefore, the GCF of Fractions 77/98,80/84,690/105 is 1/2940
Least Common Multiple of 98,84,105 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 98,84,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(98,84,105) = 7
common factors(in case of two or more numbers have common factors) = 42
GCF(98,84,105) x common factors =7 x 42 = 294
LCM(98,84,105) = ( 98 × 84 × 105 ) / 294
LCM(98,84,105) = 864360 / 294
LCM(98,84,105) = 2940
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FAQs on GCF of Fractions of 77/98, 80/84, 690/105
1. What is the HCF of 77,80,690?
The HCF of 77,80,690 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 77/98, 80/84, 690/105?
Answer: GCF of Numerators as per given numbers 77/98, 80/84, 690/105 is
GCF of Numerators i.e. for 77,80,690 is 1
LCM of denominators i.e. for 98,84,105 is 2940.
Thus, GCF of Fractions is 1/2940.Finally, GCF of Fractions for 77/98, 80/84, 690/105 is 1/2940.