GCF of 164/21, 567/252
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 164/21, 567/252 i.e 1/252 easily. The following is the detailed procedure to determine the greatest common factor of fractions 164/21, 567/252.
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 164/21,567/252?
Given fractions are 164/21,567/252
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 164/21,567/252, numerators are 164,567
Denominators are 21,252
The GCF of 164,567 is 1 .
LCM of 21,252 is 252.
The greatest common factor of 164/21,567/252 = [GCF of 164,567]/[LCM of 21,252]= 1/252
Therefore, the GCF of 164/21,567/252 is 1/252.
To find the highest common factor of 164,567, we have to find the factors of both numbers and list the highest common factor.
The factors of 164 are 1, 2, 4, 41, 82, 164
The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567
The HCF of 164,567 is 1.
Lets's calculate GCF of 164,567
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 164,567 By Matching Biggest Common Factor Method
Now, list down the factors of 164
:1,2,4,41,82,164
Now, list down the factors of 567
:1,3,7,9,21,27,63,81,189,567
Greatest Common Factor
We found the factors 164,567 . The biggest common factor number is the GCF number.
So the greatest common factor 164,567 is 1.
Lets's calculate LCM of 21,252
| 3 | 21, 252 |
| 7 | 7, 84 |
| 1, 12 |
∴ So the LCM of the given numbers is 3 x 7 x 1 x 12 = 252
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/252
Therefore, the GCF of Fractions 164/21,567/252 is 1/252
Least Common Multiple of 21,252 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 21,252 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,252) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(21,252) x common factors =21 x 1 = 21
LCM(21,252) = ( 21 × 252 ) / 21
LCM(21,252) = 5292 / 21
LCM(21,252) = 252
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FAQs on GCF of Fractions of 164/21, 567/252
1. What is the HCF of 164,567?
The HCF of 164,567 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 164/21, 567/252?
Answer: GCF of Numerators as per given numbers 164/21, 567/252 is
GCF of Numerators i.e. for 164,567 is 1
LCM of denominators i.e. for 21,252 is 252.
Thus, GCF of Fractions is 1/252.Finally, GCF of Fractions for 164/21, 567/252 is 1/252.