Factorisation Related Question

  • MHB
  • Thread starter PeterJ1
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In summary, the conversation discusses a question about factoring large numbers and comparing two calculations. The first calculation involves factorizing a number with 1050 digits, while the second calculation involves multiplying primes sequentially until the product is close to the given number. The person asks if the second calculation would be significantly easier than the first and how many digits a number would have to have for factorization to become a problem. They also mention a reference to a 232-digit number that took two years to factorize. The person realizes that the second question is obvious and considers it answered.
  • #1
PeterJ1
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A slightly odd layman's question about factoring large numbers and comparing two calculations.

Call N a number with 1050 digits.

1) Factorise N
2) Multiply the primes sequentially from 2 onwards until the product is as close as possible to N.

Would calculation 2 be significantly easier computationally than calculation 1?

How many digits would a number has to have before factorisation becomes a problem for our current methods?

Thanks
 
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  • #3
Thanks Greg.

"... to factor a 232-digit number (RSA-768) utilizing hundreds of machines took two years and the researchers estimated that a 1024-bit RSA modulus would take about a thousand times as long.[1]"

This helps with the second question but not the first, which is my main question.
 
  • #4
Doh! On reflection the answer to the second question is obvious. Consider it answered.
 

FAQ: Factorisation Related Question

What is factorisation and why is it important?

Factorisation is the process of breaking down a mathematical expression or number into its factors, which are numbers that can be multiplied together to get the original expression or number. It is important because it allows us to simplify and solve complex equations and understand the relationships between numbers.

What are the different methods of factorisation?

The most commonly used methods of factorisation are the trial and error method, the grouping method, and the quadratic formula. Other methods include the difference of squares, completing the square, and the rational root theorem.

How do you know when an expression or number is fully factorised?

An expression or number is fully factorised when it cannot be simplified any further. This means that all of the factors are prime numbers and there are no common factors left to be simplified.

Can you factorise negative numbers?

Yes, negative numbers can be factorised just like positive numbers. However, it is important to keep track of the negative signs and distribute them correctly when factoring.

How can factorisation be used in real life?

Factorisation is used in various fields of science and technology, such as cryptography, coding theory, and computer graphics. In everyday life, it can be used to simplify and solve mathematical problems, such as determining the cheapest way to buy items in bulk or finding the dimensions of a room with a given area.

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