GCF of 357/574, 642/172, 208/180
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 357/574, 642/172, 208/180 i.e 1/2221380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 357/574, 642/172, 208/180.
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 357/574,642/172,208/180?
Given fractions are 357/574,642/172,208/180
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 357/574,642/172,208/180, numerators are 357,642,208
Denominators are 574,172,180
The GCF of 357,642,208 is 1 .
LCM of 574,172,180 is 2221380.
The greatest common factor of 357/574,642/172,208/180 = [GCF of 357,642,208]/[LCM of 574,172,180]= 1/2221380
Therefore, the GCF of 357/574,642/172,208/180 is 1/2221380.
To find the highest common factor of 357,642,208, we have to find the factors of both numbers and list the highest common factor.
The factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357
The factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The HCF of 357,642,208 is 1.
Lets's calculate GCF of 357,642,208
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 357,642,208 By Matching Biggest Common Factor Method
Now, list down the factors of 357
:1,3,7,17,21,51,119,357
Now, list down the factors of 642
:1,2,3,6,107,214,321,642
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Greatest Common Factor
We found the factors 357,642,208 . The biggest common factor number is the GCF number.
So the greatest common factor 357,642,208 is 1.
Lets's calculate LCM of 574,172,180
| 2 | 574, 172, 180 |
| 2 | 287, 86, 90 |
| 287, 43, 45 |
∴ So the LCM of the given numbers is 2 x 2 x 287 x 43 x 45 = 2221380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2221380
Therefore, the GCF of Fractions 357/574,642/172,208/180 is 1/2221380
Least Common Multiple of 574,172,180 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 574,172,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(574,172,180) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(574,172,180) x common factors =2 x 4 = 8
LCM(574,172,180) = ( 574 × 172 × 180 ) / 8
LCM(574,172,180) = 17771040 / 8
LCM(574,172,180) = 2221380
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FAQs on GCF of Fractions of 357/574, 642/172, 208/180
1. What is the HCF of 357,642,208?
The HCF of 357,642,208 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 357/574, 642/172, 208/180?
Answer: GCF of Numerators as per given numbers 357/574, 642/172, 208/180 is
GCF of Numerators i.e. for 357,642,208 is 1
LCM of denominators i.e. for 574,172,180 is 2221380.
Thus, GCF of Fractions is 1/2221380.Finally, GCF of Fractions for 357/574, 642/172, 208/180 is 1/2221380.