GCF of 72/186, 21/465, 252/435
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 72/186, 21/465, 252/435 i.e 3/26970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 72/186, 21/465, 252/435.
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 72/186,21/465,252/435?
Given fractions are 72/186,21/465,252/435
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 72/186,21/465,252/435, numerators are 72,21,252
Denominators are 186,465,435
The GCF of 72,21,252 is 3 .
LCM of 186,465,435 is 26970.
The greatest common factor of 72/186,21/465,252/435 = [GCF of 72,21,252]/[LCM of 186,465,435]= 3/26970
Therefore, the GCF of 72/186,21/465,252/435 is 3/26970.
To find the highest common factor of 72,21,252, we have to find the factors of both numbers and list the highest common factor.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 21 are 1, 3, 7, 21
The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
The HCF of 72,21,252 is 3.
Lets's calculate GCF of 72,21,252
| 3 | 72, 21, 252 |
| 24, 7, 84 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 72,21,252 By Matching Biggest Common Factor Method
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 252
:1,2,3,4,6,7,9,12,14,18,21,28,36,42,63,84,126,252
Greatest Common Factor
We found the factors 72,21,252 . The biggest common factor number is the GCF number.
So the greatest common factor 72,21,252 is 3.
Lets's calculate LCM of 186,465,435
| 3 | 186, 465, 435 |
| 5 | 62, 155, 145 |
| 31 | 62, 31, 29 |
| 2, 1, 29 |
∴ So the LCM of the given numbers is 3 x 5 x 31 x 2 x 1 x 29 = 26970
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/26970
Therefore, the GCF of Fractions 72/186,21/465,252/435 is 3/26970
Least Common Multiple of 186,465,435 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 186,465,435 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(186,465,435) = 3
common factors(in case of two or more numbers have common factors) = 465
GCF(186,465,435) x common factors =3 x 465 = 1395
LCM(186,465,435) = ( 186 × 465 × 435 ) / 1395
LCM(186,465,435) = 37623150 / 1395
LCM(186,465,435) = 26970
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FAQs on GCF of Fractions of 72/186, 21/465, 252/435
1. What is the HCF of 72,21,252?
The HCF of 72,21,252 is 3
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 72/186, 21/465, 252/435?
Answer: GCF of Numerators as per given numbers 72/186, 21/465, 252/435 is
GCF of Numerators i.e. for 72,21,252 is 3
LCM of denominators i.e. for 186,465,435 is 26970.
Thus, GCF of Fractions is 3/26970.Finally, GCF of Fractions for 72/186, 21/465, 252/435 is 3/26970.