Prove 9999999+1999000 is Composite Number

MHB
Thread starter anemone
Start date Nov 20, 2020
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Composite

In summary, a composite number is a positive integer with more than two factors. To prove this, we can find two distinct numbers that evenly divide the given number. For 9999999+1999000, its factors include 1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333, 9999, 11111, 33333, 99999, 111111, 333333, 999999, 1111111, 3333333, 9999999, 1999000, and 9999999+1999000. This number can also be divided by other numbers,

Nov 20, 2020

anemone

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MHB

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Prove that the number $9999999+1999000$ is composite.

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Nov 21, 2020

kaliprasad

Gold Member

MHB

Let x = 1000 to keep it simple
So we get
$9999999+1999000 = 10^7-1 + 1999 * 1000$
$= 10 * 10^ 6 - 1+ (2000-1)* 1000$
$= 10 x^2 - 1 + (2x-1) x$ putting 1000 = x
$=12x^2 - x - 1$
$= (4x+1)(3x-1)$
$= 4001 * 2999$ putting back x = 1000

Hence it is composite

Last edited: Nov 21, 2020

1. What is a composite number?

A composite number is a positive integer that has more than two divisors, meaning it can be evenly divided by numbers other than 1 and itself.

2. How do you prove that a number is composite?

To prove that a number is composite, you must show that it has at least three divisors. This can be done by finding two numbers other than 1 and itself that divide evenly into the number, or by showing that the number is a multiple of a prime number.

3. What is the formula for determining if a number is composite?

The formula for determining if a number is composite is to check if it has any divisors other than 1 and itself. If it does, then it is composite. If it only has 1 and itself as divisors, then it is a prime number.

4. How do you prove that 9999999+1999000 is a composite number?

To prove that 9999999+1999000 is a composite number, we can first simplify the expression to 11998999. Then, we can find two numbers that divide evenly into 11998999, such as 3 and 3999667. This shows that 11998999 has at least three divisors and is therefore a composite number.

5. Can a number be both prime and composite?

No, a number cannot be both prime and composite. A prime number has exactly two divisors (1 and itself), while a composite number has more than two divisors. Therefore, a number cannot have both properties at the same time.