GCF of 976/762, 1648/734
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 976/762, 1648/734 i.e 16/279654 easily. The following is the detailed procedure to determine the greatest common factor of fractions 976/762, 1648/734.
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 976/762,1648/734?
Given fractions are 976/762,1648/734
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 976/762,1648/734, numerators are 976,1648
Denominators are 762,734
The GCF of 976,1648 is 16 .
LCM of 762,734 is 279654.
The greatest common factor of 976/762,1648/734 = [GCF of 976,1648]/[LCM of 762,734]= 16/279654
Therefore, the GCF of 976/762,1648/734 is 16/279654.
To find the highest common factor of 976,1648, we have to find the factors of both numbers and list the highest common factor.
The factors of 976 are 1, 2, 4, 8, 16, 61, 122, 244, 488, 976
The factors of 1648 are 1, 2, 4, 8, 16, 103, 206, 412, 824, 1648
The HCF of 976,1648 is 16.
Lets's calculate GCF of 976,1648
| 2 | 976, 1648 |
| 2 | 488, 824 |
| 2 | 244, 412 |
| 2 | 122, 206 |
| 61, 103 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 976,1648 By Matching Biggest Common Factor Method
Now, list down the factors of 976
:1,2,4,8,16,61,122,244,488,976
Now, list down the factors of 1648
:1,2,4,8,16,103,206,412,824,1648
Greatest Common Factor
We found the factors 976,1648 . The biggest common factor number is the GCF number.
So the greatest common factor 976,1648 is 16.
Lets's calculate LCM of 762,734
| 2 | 762, 734 |
| 381, 367 |
∴ So the LCM of the given numbers is 2 x 381 x 367 = 279654
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/279654
Therefore, the GCF of Fractions 976/762,1648/734 is 16/279654
Least Common Multiple of 762,734 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 762,734 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(762,734) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(762,734) x common factors =2 x 1 = 2
LCM(762,734) = ( 762 × 734 ) / 2
LCM(762,734) = 559308 / 2
LCM(762,734) = 279654
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FAQs on GCF of Fractions of 976/762, 1648/734
1. What is the HCF of 976,1648?
The HCF of 976,1648 is 16
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 976/762, 1648/734?
Answer: GCF of Numerators as per given numbers 976/762, 1648/734 is
GCF of Numerators i.e. for 976,1648 is 16
LCM of denominators i.e. for 762,734 is 279654.
Thus, GCF of Fractions is 16/279654.Finally, GCF of Fractions for 976/762, 1648/734 is 16/279654.