GCF of 432/966, 6400/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 432/966, 6400/214 i.e 16/103362 easily. The following is the detailed procedure to determine the greatest common factor of fractions 432/966, 6400/214.
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 432/966,6400/214?
Given fractions are 432/966,6400/214
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 432/966,6400/214, numerators are 432,6400
Denominators are 966,214
The GCF of 432,6400 is 16 .
LCM of 966,214 is 103362.
The greatest common factor of 432/966,6400/214 = [GCF of 432,6400]/[LCM of 966,214]= 16/103362
Therefore, the GCF of 432/966,6400/214 is 16/103362.
To find the highest common factor of 432,6400, we have to find the factors of both numbers and list the highest common factor.
The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
The factors of 6400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 640, 800, 1280, 1600, 3200, 6400
The HCF of 432,6400 is 16.
Lets's calculate GCF of 432,6400
| 2 | 432, 6400 |
| 2 | 216, 3200 |
| 2 | 108, 1600 |
| 2 | 54, 800 |
| 27, 400 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 432,6400 By Matching Biggest Common Factor Method
Now, list down the factors of 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
Now, list down the factors of 6400
:1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,128,160,200,256,320,400,640,800,1280,1600,3200,6400
Greatest Common Factor
We found the factors 432,6400 . The biggest common factor number is the GCF number.
So the greatest common factor 432,6400 is 16.
Lets's calculate LCM of 966,214
| 2 | 966, 214 |
| 483, 107 |
∴ So the LCM of the given numbers is 2 x 483 x 107 = 103362
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/103362
Therefore, the GCF of Fractions 432/966,6400/214 is 16/103362
Least Common Multiple of 966,214 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 966,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(966,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(966,214) x common factors =2 x 1 = 2
LCM(966,214) = ( 966 × 214 ) / 2
LCM(966,214) = 206724 / 2
LCM(966,214) = 103362
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FAQs on GCF of Fractions of 432/966, 6400/214
1. What is the HCF of 432,6400?
The HCF of 432,6400 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 432/966, 6400/214?
Answer: GCF of Numerators as per given numbers 432/966, 6400/214 is
GCF of Numerators i.e. for 432,6400 is 16
LCM of denominators i.e. for 966,214 is 103362.
Thus, GCF of Fractions is 16/103362.Finally, GCF of Fractions for 432/966, 6400/214 is 16/103362.