GCF of 84/74, 714/82, 777/592
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 84/74, 714/82, 777/592 i.e 21/24272 easily. The following is the detailed procedure to determine the greatest common factor of fractions 84/74, 714/82, 777/592.
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 84/74,714/82,777/592?
Given fractions are 84/74,714/82,777/592
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 84/74,714/82,777/592, numerators are 84,714,777
Denominators are 74,82,592
The GCF of 84,714,777 is 21 .
LCM of 74,82,592 is 24272.
The greatest common factor of 84/74,714/82,777/592 = [GCF of 84,714,777]/[LCM of 74,82,592]= 21/24272
Therefore, the GCF of 84/74,714/82,777/592 is 21/24272.
To find the highest common factor of 84,714,777, we have to find the factors of both numbers and list the highest common factor.
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The factors of 777 are 1, 3, 7, 21, 37, 111, 259, 777
The HCF of 84,714,777 is 21.
Lets's calculate GCF of 84,714,777
| 3 | 84, 714, 777 |
| 7 | 28, 238, 259 |
| 4, 34, 37 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 84,714,777 By Matching Biggest Common Factor Method
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Now, list down the factors of 777
:1,3,7,21,37,111,259,777
Greatest Common Factor
We found the factors 84,714,777 . The biggest common factor number is the GCF number.
So the greatest common factor 84,714,777 is 21.
Lets's calculate LCM of 74,82,592
| 2 | 74, 82, 592 |
| 37 | 37, 41, 296 |
| 1, 41, 8 |
∴ So the LCM of the given numbers is 2 x 37 x 1 x 41 x 8 = 24272
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/24272
Therefore, the GCF of Fractions 84/74,714/82,777/592 is 21/24272
Least Common Multiple of 74,82,592 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 74,82,592 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,82,592) = 2
common factors(in case of two or more numbers have common factors) = 74
GCF(74,82,592) x common factors =2 x 74 = 148
LCM(74,82,592) = ( 74 × 82 × 592 ) / 148
LCM(74,82,592) = 3592256 / 148
LCM(74,82,592) = 24272
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FAQs on GCF of Fractions of 84/74, 714/82, 777/592
1. What is the HCF of 84,714,777?
The HCF of 84,714,777 is 21
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 84/74, 714/82, 777/592?
Answer: GCF of Numerators as per given numbers 84/74, 714/82, 777/592 is
GCF of Numerators i.e. for 84,714,777 is 21
LCM of denominators i.e. for 74,82,592 is 24272.
Thus, GCF of Fractions is 21/24272.Finally, GCF of Fractions for 84/74, 714/82, 777/592 is 21/24272.