GCF of 30/343, 90/996, 711/714
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/343, 90/996, 711/714 i.e 3/5807676 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/343, 90/996, 711/714.
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 30/343,90/996,711/714?
Given fractions are 30/343,90/996,711/714
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 30/343,90/996,711/714, numerators are 30,90,711
Denominators are 343,996,714
The GCF of 30,90,711 is 3 .
LCM of 343,996,714 is 5807676.
The greatest common factor of 30/343,90/996,711/714 = [GCF of 30,90,711]/[LCM of 343,996,714]= 3/5807676
Therefore, the GCF of 30/343,90/996,711/714 is 3/5807676.
To find the highest common factor of 30,90,711, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The factors of 711 are 1, 3, 9, 79, 237, 711
The HCF of 30,90,711 is 3.
Lets's calculate GCF of 30,90,711
| 3 | 30, 90, 711 |
| 10, 30, 237 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 30,90,711 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 90
:1,2,3,5,6,9,10,15,18,30,45,90
Now, list down the factors of 711
:1,3,9,79,237,711
Greatest Common Factor
We found the factors 30,90,711 . The biggest common factor number is the GCF number.
So the greatest common factor 30,90,711 is 3.
Lets's calculate LCM of 343,996,714
| 2 | 343, 996, 714 |
| 3 | 343, 498, 357 |
| 7 | 343, 166, 119 |
| 49, 166, 17 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 49 x 166 x 17 = 5807676
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/5807676
Therefore, the GCF of Fractions 30/343,90/996,711/714 is 3/5807676
Least Common Multiple of 343,996,714 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 343,996,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(343,996,714) = 1
common factors(in case of two or more numbers have common factors) = 42
GCF(343,996,714) x common factors =1 x 42 = 42
LCM(343,996,714) = ( 343 × 996 × 714 ) / 42
LCM(343,996,714) = 243922392 / 42
LCM(343,996,714) = 5807676
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FAQs on GCF of Fractions of 30/343, 90/996, 711/714
1. What is the HCF of 30,90,711?
The HCF of 30,90,711 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 30/343, 90/996, 711/714?
Answer: GCF of Numerators as per given numbers 30/343, 90/996, 711/714 is
GCF of Numerators i.e. for 30,90,711 is 3
LCM of denominators i.e. for 343,996,714 is 5807676.
Thus, GCF of Fractions is 3/5807676.Finally, GCF of Fractions for 30/343, 90/996, 711/714 is 3/5807676.