GCF of 972/784, 7641/5214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 972/784, 7641/5214 i.e 27/2043888 easily. The following is the detailed procedure to determine the greatest common factor of fractions 972/784, 7641/5214.
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 972/784,7641/5214?
Given fractions are 972/784,7641/5214
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 972/784,7641/5214, numerators are 972,7641
Denominators are 784,5214
The GCF of 972,7641 is 27 .
LCM of 784,5214 is 2043888.
The greatest common factor of 972/784,7641/5214 = [GCF of 972,7641]/[LCM of 784,5214]= 27/2043888
Therefore, the GCF of 972/784,7641/5214 is 27/2043888.
To find the highest common factor of 972,7641, we have to find the factors of both numbers and list the highest common factor.
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The factors of 7641 are 1, 3, 9, 27, 283, 849, 2547, 7641
The HCF of 972,7641 is 27.
Lets's calculate GCF of 972,7641
| 3 | 972, 7641 |
| 3 | 324, 2547 |
| 3 | 108, 849 |
| 36, 283 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Greatest Common Factor of 972,7641 By Matching Biggest Common Factor Method
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Now, list down the factors of 7641
:1,3,9,27,283,849,2547,7641
Greatest Common Factor
We found the factors 972,7641 . The biggest common factor number is the GCF number.
So the greatest common factor 972,7641 is 27.
Lets's calculate LCM of 784,5214
| 2 | 784, 5214 |
| 392, 2607 |
∴ So the LCM of the given numbers is 2 x 392 x 2607 = 2043888
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/2043888
Therefore, the GCF of Fractions 972/784,7641/5214 is 27/2043888
Least Common Multiple of 784,5214 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 784,5214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(784,5214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(784,5214) x common factors =2 x 1 = 2
LCM(784,5214) = ( 784 × 5214 ) / 2
LCM(784,5214) = 4087776 / 2
LCM(784,5214) = 2043888
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 972/784, 7641/5214
1. What is the HCF of 972,7641?
The HCF of 972,7641 is 27
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 972/784, 7641/5214?
Answer: GCF of Numerators as per given numbers 972/784, 7641/5214 is
GCF of Numerators i.e. for 972,7641 is 27
LCM of denominators i.e. for 784,5214 is 2043888.
Thus, GCF of Fractions is 27/2043888.Finally, GCF of Fractions for 972/784, 7641/5214 is 27/2043888.