GCF of 7000/233, 7784/932
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7000/233, 7784/932 i.e 56/932 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7000/233, 7784/932.
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 7000/233,7784/932?
Given fractions are 7000/233,7784/932
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 7000/233,7784/932, numerators are 7000,7784
Denominators are 233,932
The GCF of 7000,7784 is 56 .
LCM of 233,932 is 932.
The greatest common factor of 7000/233,7784/932 = [GCF of 7000,7784]/[LCM of 233,932]= 56/932
Therefore, the GCF of 7000/233,7784/932 is 56/932.
To find the highest common factor of 7000,7784, we have to find the factors of both numbers and list the highest common factor.
The factors of 7000 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, 7000
The factors of 7784 are 1, 2, 4, 7, 8, 14, 28, 56, 139, 278, 556, 973, 1112, 1946, 3892, 7784
The HCF of 7000,7784 is 56.
Lets's calculate GCF of 7000,7784
| 2 | 7000, 7784 |
| 2 | 3500, 3892 |
| 2 | 1750, 1946 |
| 7 | 875, 973 |
| 125, 139 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 7 = 56
Greatest Common Factor of 7000,7784 By Matching Biggest Common Factor Method
Now, list down the factors of 7000
:1,2,4,5,7,8,10,14,20,25,28,35,40,50,56,70,100,125,140,175,200,250,280,350,500,700,875,1000,1400,1750,3500,7000
Now, list down the factors of 7784
:1,2,4,7,8,14,28,56,139,278,556,973,1112,1946,3892,7784
Greatest Common Factor
We found the factors 7000,7784 . The biggest common factor number is the GCF number.
So the greatest common factor 7000,7784 is 56.
Lets's calculate LCM of 233,932
| 233 | 233, 932 |
| 1, 4 |
∴ So the LCM of the given numbers is 233 x 1 x 4 = 932
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 56/932
Therefore, the GCF of Fractions 7000/233,7784/932 is 56/932
Least Common Multiple of 233,932 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 233,932 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(233,932) = 233
common factors(in case of two or more numbers have common factors) = 1
GCF(233,932) x common factors =233 x 1 = 233
LCM(233,932) = ( 233 × 932 ) / 233
LCM(233,932) = 217156 / 233
LCM(233,932) = 932
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FAQs on GCF of Fractions of 7000/233, 7784/932
1. What is the HCF of 7000,7784?
The HCF of 7000,7784 is 56
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 7000/233, 7784/932?
Answer: GCF of Numerators as per given numbers 7000/233, 7784/932 is
GCF of Numerators i.e. for 7000,7784 is 56
LCM of denominators i.e. for 233,932 is 932.
Thus, GCF of Fractions is 56/932.Finally, GCF of Fractions for 7000/233, 7784/932 is 56/932.