GCF of 784/115, 8932/169
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 784/115, 8932/169 i.e 28/19435 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/115, 8932/169.
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 784/115,8932/169?
Given fractions are 784/115,8932/169
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 784/115,8932/169, numerators are 784,8932
Denominators are 115,169
The GCF of 784,8932 is 28 .
LCM of 115,169 is 19435.
The greatest common factor of 784/115,8932/169 = [GCF of 784,8932]/[LCM of 115,169]= 28/19435
Therefore, the GCF of 784/115,8932/169 is 28/19435.
To find the highest common factor of 784,8932, 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 8932 are 1, 2, 4, 7, 11, 14, 22, 28, 29, 44, 58, 77, 116, 154, 203, 308, 319, 406, 638, 812, 1276, 2233, 4466, 8932
The HCF of 784,8932 is 28.
Lets's calculate GCF of 784,8932
| 2 | 784, 8932 |
| 2 | 392, 4466 |
| 7 | 196, 2233 |
| 28, 319 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 784,8932 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 8932
:1,2,4,7,11,14,22,28,29,44,58,77,116,154,203,308,319,406,638,812,1276,2233,4466,8932
Greatest Common Factor
We found the factors 784,8932 . The biggest common factor number is the GCF number.
So the greatest common factor 784,8932 is 28.
Lets's calculate LCM of 115,169
Given numbers has no common factors except 1. So, there LCM is their product i.e 19435
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/19435
Therefore, the GCF of Fractions 784/115,8932/169 is 28/19435
Least Common Multiple of 115,169 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 115,169 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(115,169) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(115,169) x common factors =1 x 1 = 1
LCM(115,169) = ( 115 × 169 ) / 1
LCM(115,169) = 19435 / 1
LCM(115,169) = 19435
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FAQs on GCF of Fractions of 784/115, 8932/169
1. What is the HCF of 784,8932?
The HCF of 784,8932 is 28
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 784/115, 8932/169?
Answer: GCF of Numerators as per given numbers 784/115, 8932/169 is
GCF of Numerators i.e. for 784,8932 is 28
LCM of denominators i.e. for 115,169 is 19435.
Thus, GCF of Fractions is 28/19435.Finally, GCF of Fractions for 784/115, 8932/169 is 28/19435.