GCF of 784/917, 9730/225
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 784/917, 9730/225 i.e 14/206325 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/917, 9730/225.
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 784/917,9730/225?
Given fractions are 784/917,9730/225
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 784/917,9730/225, numerators are 784,9730
Denominators are 917,225
The GCF of 784,9730 is 14 .
LCM of 917,225 is 206325.
The greatest common factor of 784/917,9730/225 = [GCF of 784,9730]/[LCM of 917,225]= 14/206325
Therefore, the GCF of 784/917,9730/225 is 14/206325.
To find the highest common factor of 784,9730, we have to find the factors of both numbers and list the highest common factor.
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The factors of 9730 are 1, 2, 5, 7, 10, 14, 35, 70, 139, 278, 695, 973, 1390, 1946, 4865, 9730
The HCF of 784,9730 is 14.
Lets's calculate GCF of 784,9730
| 2 | 784, 9730 |
| 7 | 392, 4865 |
| 56, 695 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 784,9730 By Matching Biggest Common Factor Method
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Now, list down the factors of 9730
:1,2,5,7,10,14,35,70,139,278,695,973,1390,1946,4865,9730
Greatest Common Factor
We found the factors 784,9730 . The biggest common factor number is the GCF number.
So the greatest common factor 784,9730 is 14.
Lets's calculate LCM of 917,225
Given numbers has no common factors except 1. So, there LCM is their product i.e 206325
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/206325
Therefore, the GCF of Fractions 784/917,9730/225 is 14/206325
Least Common Multiple of 917,225 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 917,225 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(917,225) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(917,225) x common factors =1 x 1 = 1
LCM(917,225) = ( 917 × 225 ) / 1
LCM(917,225) = 206325 / 1
LCM(917,225) = 206325
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FAQs on GCF of Fractions of 784/917, 9730/225
1. What is the HCF of 784,9730?
The HCF of 784,9730 is 14
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 784/917, 9730/225?
Answer: GCF of Numerators as per given numbers 784/917, 9730/225 is
GCF of Numerators i.e. for 784,9730 is 14
LCM of denominators i.e. for 917,225 is 206325.
Thus, GCF of Fractions is 14/206325.Finally, GCF of Fractions for 784/917, 9730/225 is 14/206325.