Showing items from Number Theory

Prime Factorization of a Number

• Date : November 7, 2021
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• Tags : Number theory ,Primes ,Factors ,Algorithms ,Data structures ,Coding interview

Problem Statement How do we find all the prime factors of a given number? For example, when n = 12, the output should be [2, 3]. Notice that 1, 4, 6, 12 are also factors of 12 but they aren’t prime and therefore should be excluded from the output. Solution The following solution is …

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Find all prime numbers up to a given number

• Date : November 3, 2021
• Categories :
• Tags : Number theory ,Primes ,Algorithms ,Data structures ,Coding interview

Problem Statement How do we find all the prime numbers up to a given number? For example, when n = 10, the output should be 4 since there are 4 prime numbers less than 10, namely 2, 3, 5, 7. Naive Approach A naive approach would be to iterate from 2 to n and count the number of primes along the way:

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