GCF of 51/585, 98/229, 654/765
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 51/585, 98/229, 654/765 i.e 1/2277405 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/585, 98/229, 654/765.
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 51/585,98/229,654/765?
Given fractions are 51/585,98/229,654/765
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 51/585,98/229,654/765, numerators are 51,98,654
Denominators are 585,229,765
The GCF of 51,98,654 is 1 .
LCM of 585,229,765 is 2277405.
The greatest common factor of 51/585,98/229,654/765 = [GCF of 51,98,654]/[LCM of 585,229,765]= 1/2277405
Therefore, the GCF of 51/585,98/229,654/765 is 1/2277405.
To find the highest common factor of 51,98,654, we have to find the factors of both numbers and list the highest common factor.
The factors of 51 are 1, 3, 17, 51
The factors of 98 are 1, 2, 7, 14, 49, 98
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The HCF of 51,98,654 is 1.
Lets's calculate GCF of 51,98,654
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 51,98,654 By Matching Biggest Common Factor Method
Now, list down the factors of 51
:1,3,17,51
Now, list down the factors of 98
:1,2,7,14,49,98
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Greatest Common Factor
We found the factors 51,98,654 . The biggest common factor number is the GCF number.
So the greatest common factor 51,98,654 is 1.
Lets's calculate LCM of 585,229,765
| 3 | 585, 229, 765 |
| 3 | 195, 229, 255 |
| 5 | 65, 229, 85 |
| 13, 229, 17 |
∴ So the LCM of the given numbers is 3 x 3 x 5 x 13 x 229 x 17 = 2277405
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2277405
Therefore, the GCF of Fractions 51/585,98/229,654/765 is 1/2277405
Least Common Multiple of 585,229,765 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 585,229,765 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(585,229,765) = 1
common factors(in case of two or more numbers have common factors) = 45
GCF(585,229,765) x common factors =1 x 45 = 45
LCM(585,229,765) = ( 585 × 229 × 765 ) / 45
LCM(585,229,765) = 102483225 / 45
LCM(585,229,765) = 2277405
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FAQs on GCF of Fractions of 51/585, 98/229, 654/765
1. What is the HCF of 51,98,654?
The HCF of 51,98,654 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 51/585, 98/229, 654/765?
Answer: GCF of Numerators as per given numbers 51/585, 98/229, 654/765 is
GCF of Numerators i.e. for 51,98,654 is 1
LCM of denominators i.e. for 585,229,765 is 2277405.
Thus, GCF of Fractions is 1/2277405.Finally, GCF of Fractions for 51/585, 98/229, 654/765 is 1/2277405.