GCF of 21/670, 10/301, 728/301
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 21/670, 10/301, 728/301 i.e 1/201670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/670, 10/301, 728/301.
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 21/670,10/301,728/301?
Given fractions are 21/670,10/301,728/301
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 21/670,10/301,728/301, numerators are 21,10,728
Denominators are 670,301,301
The GCF of 21,10,728 is 1 .
LCM of 670,301,301 is 201670.
The greatest common factor of 21/670,10/301,728/301 = [GCF of 21,10,728]/[LCM of 670,301,301]= 1/201670
Therefore, the GCF of 21/670,10/301,728/301 is 1/201670.
To find the highest common factor of 21,10,728, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 10 are 1, 2, 5, 10
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The HCF of 21,10,728 is 1.
Lets's calculate GCF of 21,10,728
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 21,10,728 By Matching Biggest Common Factor Method
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 10
:1,2,5,10
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 21,10,728 . The biggest common factor number is the GCF number.
So the greatest common factor 21,10,728 is 1.
Lets's calculate LCM of 670,301,301
| 7 | 670, 301, 301 |
| 43 | 670, 43, 43 |
| 670, 1, 1 |
∴ So the LCM of the given numbers is 7 x 43 x 670 x 1 x 1 = 201670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/201670
Therefore, the GCF of Fractions 21/670,10/301,728/301 is 1/201670
Least Common Multiple of 670,301,301 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 670,301,301 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(670,301,301) = 1
common factors(in case of two or more numbers have common factors) = 301
GCF(670,301,301) x common factors =1 x 301 = 301
LCM(670,301,301) = ( 670 × 301 × 301 ) / 301
LCM(670,301,301) = 60702670 / 301
LCM(670,301,301) = 201670
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FAQs on GCF of Fractions of 21/670, 10/301, 728/301
1. What is the HCF of 21,10,728?
The HCF of 21,10,728 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 21/670, 10/301, 728/301?
Answer: GCF of Numerators as per given numbers 21/670, 10/301, 728/301 is
GCF of Numerators i.e. for 21,10,728 is 1
LCM of denominators i.e. for 670,301,301 is 201670.
Thus, GCF of Fractions is 1/201670.Finally, GCF of Fractions for 21/670, 10/301, 728/301 is 1/201670.