GCF of 132/712, 538/256
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 132/712, 538/256 i.e 2/22784 easily. The following is the detailed procedure to determine the greatest common factor of fractions 132/712, 538/256.
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 132/712,538/256?
Given fractions are 132/712,538/256
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 132/712,538/256, numerators are 132,538
Denominators are 712,256
The GCF of 132,538 is 2 .
LCM of 712,256 is 22784.
The greatest common factor of 132/712,538/256 = [GCF of 132,538]/[LCM of 712,256]= 2/22784
Therefore, the GCF of 132/712,538/256 is 2/22784.
To find the highest common factor of 132,538, we have to find the factors of both numbers and list the highest common factor.
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The factors of 538 are 1, 2, 269, 538
The HCF of 132,538 is 2.
Lets's calculate GCF of 132,538
| 2 | 132, 538 |
| 66, 269 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 132,538 By Matching Biggest Common Factor Method
Now, list down the factors of 132
:1,2,3,4,6,11,12,22,33,44,66,132
Now, list down the factors of 538
:1,2,269,538
Greatest Common Factor
We found the factors 132,538 . The biggest common factor number is the GCF number.
So the greatest common factor 132,538 is 2.
Lets's calculate LCM of 712,256
| 2 | 712, 256 |
| 2 | 356, 128 |
| 2 | 178, 64 |
| 89, 32 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 89 x 32 = 22784
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/22784
Therefore, the GCF of Fractions 132/712,538/256 is 2/22784
Least Common Multiple of 712,256 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 712,256 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(712,256) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(712,256) x common factors =8 x 1 = 8
LCM(712,256) = ( 712 × 256 ) / 8
LCM(712,256) = 182272 / 8
LCM(712,256) = 22784
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FAQs on GCF of Fractions of 132/712, 538/256
1. What is the HCF of 132,538?
The HCF of 132,538 is 2
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 132/712, 538/256?
Answer: GCF of Numerators as per given numbers 132/712, 538/256 is
GCF of Numerators i.e. for 132,538 is 2
LCM of denominators i.e. for 712,256 is 22784.
Thus, GCF of Fractions is 2/22784.Finally, GCF of Fractions for 132/712, 538/256 is 2/22784.