GCF of 21/77, 178/19, 221/464
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 21/77, 178/19, 221/464 i.e 1/678832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/77, 178/19, 221/464.
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 21/77,178/19,221/464?
Given fractions are 21/77,178/19,221/464
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 21/77,178/19,221/464, numerators are 21,178,221
Denominators are 77,19,464
The GCF of 21,178,221 is 1 .
LCM of 77,19,464 is 678832.
The greatest common factor of 21/77,178/19,221/464 = [GCF of 21,178,221]/[LCM of 77,19,464]= 1/678832
Therefore, the GCF of 21/77,178/19,221/464 is 1/678832.
To find the highest common factor of 21,178,221, 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 178 are 1, 2, 89, 178
The factors of 221 are 1, 13, 17, 221
The HCF of 21,178,221 is 1.
Lets's calculate GCF of 21,178,221
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 21,178,221 By Matching Biggest Common Factor Method
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 178
:1,2,89,178
Now, list down the factors of 221
:1,13,17,221
Greatest Common Factor
We found the factors 21,178,221 . The biggest common factor number is the GCF number.
So the greatest common factor 21,178,221 is 1.
Lets's calculate LCM of 77,19,464
Given numbers has no common factors except 1. So, there LCM is their product i.e 678832
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/678832
Therefore, the GCF of Fractions 21/77,178/19,221/464 is 1/678832
Least Common Multiple of 77,19,464 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 77,19,464 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,19,464) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(77,19,464) x common factors =1 x 1 = 1
LCM(77,19,464) = ( 77 × 19 × 464 ) / 1
LCM(77,19,464) = 678832 / 1
LCM(77,19,464) = 678832
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FAQs on GCF of Fractions of 21/77, 178/19, 221/464
1. What is the HCF of 21,178,221?
The HCF of 21,178,221 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 21/77, 178/19, 221/464?
Answer: GCF of Numerators as per given numbers 21/77, 178/19, 221/464 is
GCF of Numerators i.e. for 21,178,221 is 1
LCM of denominators i.e. for 77,19,464 is 678832.
Thus, GCF of Fractions is 1/678832.Finally, GCF of Fractions for 21/77, 178/19, 221/464 is 1/678832.