A question about factoring and factors

In summary, the conversation discusses the possibility of determining the other digits of the factors of a given number N, where only the last digits of the two factors are known. It is suggested that if N is large enough and the factors are expressed as 100m + r and 100n + s, where r and s are less than 100, there is only one equation with two unknowns and it is difficult to find a solution in general. It is then questioned what is the minimum number of digits that should be known in order to determine the factors.
  • #1
epsi00
84
0
say we have a number N=pq (known) and we only know the last digits of the two factors p and q ( the righter most digit of each factor ). Is-it possible to determine the other digits of the factors? If not, what is the minimum number of digits that should be known before the answer can be a yes?
 
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  • #2
If N is big enough, I suspect the answer is no.
Let p=100m + r, q=100n + s, where r,s < 100 (all integers).
Then N = 10000mn + 100 (ms + nr) + rs.
You now have one equation (N=) with 2 unknowns (m and n). I don't believe you can find a solution in general.
 

1. What is factoring?

Factoring is the process of breaking down a larger number into its smaller, multiply-able components. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because they can all be multiplied together to equal 12.

2. Why is factoring important?

Factoring is important because it helps us simplify and solve more complex mathematical equations. It also has many real-world applications, such as in finance and cryptography.

3. How do I find the factors of a number?

To find the factors of a number, you can start by listing out the first few numbers and their products until you find all the factors. Alternatively, you can use a factor tree or a calculator to help you determine the factors.

4. What is the difference between a factor and a multiple?

A factor is a number that can be multiplied with another number to get a specific product, while a multiple is the result of multiplying a number by an integer. For example, the factors of 6 are 1, 2, 3, and 6, while the multiples of 6 are 6, 12, 18, etc.

5. How can factoring be used to solve equations?

Factoring can be used to solve equations by breaking down a larger equation into smaller, simpler factors. This can help us find the roots or solutions of the equation, which can then be used to solve for the unknown variable.

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