GCF of 402/24, 757/72, 132/12
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 402/24, 757/72, 132/12 i.e 1/72 easily. The following is the detailed procedure to determine the greatest common factor of fractions 402/24, 757/72, 132/12.
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 402/24,757/72,132/12?
Given fractions are 402/24,757/72,132/12
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 402/24,757/72,132/12, numerators are 402,757,132
Denominators are 24,72,12
The GCF of 402,757,132 is 1 .
LCM of 24,72,12 is 72.
The greatest common factor of 402/24,757/72,132/12 = [GCF of 402,757,132]/[LCM of 24,72,12]= 1/72
Therefore, the GCF of 402/24,757/72,132/12 is 1/72.
To find the highest common factor of 402,757,132, we have to find the factors of both numbers and list the highest common factor.
The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402
The factors of 757 are 1, 757
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The HCF of 402,757,132 is 1.
Lets's calculate GCF of 402,757,132
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 402,757,132 By Matching Biggest Common Factor Method
Now, list down the factors of 402
:1,2,3,6,67,134,201,402
Now, list down the factors of 757
:1,757
Now, list down the factors of 132
:1,2,3,4,6,11,12,22,33,44,66,132
Greatest Common Factor
We found the factors 402,757,132 . The biggest common factor number is the GCF number.
So the greatest common factor 402,757,132 is 1.
Lets's calculate LCM of 24,72,12
| 2 | 24, 72, 12 |
| 2 | 12, 36, 6 |
| 2 | 3, 18, 6 |
| 3 | 3, 9, 3 |
| 1, 1, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 1 x 3 = 72
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/72
Therefore, the GCF of Fractions 402/24,757/72,132/12 is 1/72
Least Common Multiple of 24,72,12 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 24,72,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,72,12) = 12
common factors(in case of two or more numbers have common factors) = 24
GCF(24,72,12) x common factors =12 x 24 = 288
LCM(24,72,12) = ( 24 × 72 × 12 ) / 288
LCM(24,72,12) = 20736 / 288
LCM(24,72,12) = 72
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FAQs on GCF of Fractions of 402/24, 757/72, 132/12
1. What is the HCF of 402,757,132?
The HCF of 402,757,132 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 402/24, 757/72, 132/12?
Answer: GCF of Numerators as per given numbers 402/24, 757/72, 132/12 is
GCF of Numerators i.e. for 402,757,132 is 1
LCM of denominators i.e. for 24,72,12 is 72.
Thus, GCF of Fractions is 1/72.Finally, GCF of Fractions for 402/24, 757/72, 132/12 is 1/72.