GCF of 40/81, 30/714, 294/914
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 40/81, 30/714, 294/914 i.e 2/8810046 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/81, 30/714, 294/914.
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 40/81,30/714,294/914?
Given fractions are 40/81,30/714,294/914
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 40/81,30/714,294/914, numerators are 40,30,294
Denominators are 81,714,914
The GCF of 40,30,294 is 2 .
LCM of 81,714,914 is 8810046.
The greatest common factor of 40/81,30/714,294/914 = [GCF of 40,30,294]/[LCM of 81,714,914]= 2/8810046
Therefore, the GCF of 40/81,30/714,294/914 is 2/8810046.
To find the highest common factor of 40,30,294, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The HCF of 40,30,294 is 2.
Lets's calculate GCF of 40,30,294
| 2 | 40, 30, 294 |
| 20, 15, 147 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 40,30,294 By Matching Biggest Common Factor Method
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Greatest Common Factor
We found the factors 40,30,294 . The biggest common factor number is the GCF number.
So the greatest common factor 40,30,294 is 2.
Lets's calculate LCM of 81,714,914
| 2 | 81, 714, 914 |
| 3 | 81, 357, 457 |
| 27, 119, 457 |
∴ So the LCM of the given numbers is 2 x 3 x 27 x 119 x 457 = 8810046
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/8810046
Therefore, the GCF of Fractions 40/81,30/714,294/914 is 2/8810046
Least Common Multiple of 81,714,914 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 81,714,914 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,714,914) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(81,714,914) x common factors =1 x 6 = 6
LCM(81,714,914) = ( 81 × 714 × 914 ) / 6
LCM(81,714,914) = 52860276 / 6
LCM(81,714,914) = 8810046
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FAQs on GCF of Fractions of 40/81, 30/714, 294/914
1. What is the HCF of 40,30,294?
The HCF of 40,30,294 is 2
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 40/81, 30/714, 294/914?
Answer: GCF of Numerators as per given numbers 40/81, 30/714, 294/914 is
GCF of Numerators i.e. for 40,30,294 is 2
LCM of denominators i.e. for 81,714,914 is 8810046.
Thus, GCF of Fractions is 2/8810046.Finally, GCF of Fractions for 40/81, 30/714, 294/914 is 2/8810046.