GCF of 564/42, 136/21, 825/12
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 564/42, 136/21, 825/12 i.e 1/84 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/42, 136/21, 825/12.
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 564/42,136/21,825/12?
Given fractions are 564/42,136/21,825/12
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 564/42,136/21,825/12, numerators are 564,136,825
Denominators are 42,21,12
The GCF of 564,136,825 is 1 .
LCM of 42,21,12 is 84.
The greatest common factor of 564/42,136/21,825/12 = [GCF of 564,136,825]/[LCM of 42,21,12]= 1/84
Therefore, the GCF of 564/42,136/21,825/12 is 1/84.
To find the highest common factor of 564,136,825, we have to find the factors of both numbers and list the highest common factor.
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136
The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
The HCF of 564,136,825 is 1.
Lets's calculate GCF of 564,136,825
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 564,136,825 By Matching Biggest Common Factor Method
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Now, list down the factors of 136
:1,2,4,8,17,34,68,136
Now, list down the factors of 825
:1,3,5,11,15,25,33,55,75,165,275,825
Greatest Common Factor
We found the factors 564,136,825 . The biggest common factor number is the GCF number.
So the greatest common factor 564,136,825 is 1.
Lets's calculate LCM of 42,21,12
| 2 | 42, 21, 12 |
| 3 | 21, 21, 6 |
| 7 | 7, 7, 2 |
| 1, 1, 2 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 1 x 1 x 2 = 84
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/84
Therefore, the GCF of Fractions 564/42,136/21,825/12 is 1/84
Least Common Multiple of 42,21,12 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 42,21,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,21,12) = 3
common factors(in case of two or more numbers have common factors) = 42
GCF(42,21,12) x common factors =3 x 42 = 126
LCM(42,21,12) = ( 42 × 21 × 12 ) / 126
LCM(42,21,12) = 10584 / 126
LCM(42,21,12) = 84
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FAQs on GCF of Fractions of 564/42, 136/21, 825/12
1. What is the HCF of 564,136,825?
The HCF of 564,136,825 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 564/42, 136/21, 825/12?
Answer: GCF of Numerators as per given numbers 564/42, 136/21, 825/12 is
GCF of Numerators i.e. for 564,136,825 is 1
LCM of denominators i.e. for 42,21,12 is 84.
Thus, GCF of Fractions is 1/84.Finally, GCF of Fractions for 564/42, 136/21, 825/12 is 1/84.