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"Therefore, if you have the number's factorization (see [problem 3](https://projecteuler.net/problem=3)), you can use it to compute the sum of its divisors.\n",
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"Therefore, if you have the number's factorization (see [problem 3](https://projecteuler.net/problem=3)), you can use it to compute the sum of its divisors.\n",
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"\n",
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"\n",
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"## Avoiding factoring\n",
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"## Avoiding factoring\n",
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"Since we need all the sums of divisors up to 10000, instead of factoring each number individually, we can compute each value of $\\sigma$ in a loop, once again taking advantage of $\\sigma$ being multiplicative. (In some ways, this method is similar to the sieve of Eratosthenes - see [problem 10](https://projecteuler.net/problem=10))"
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"Since we need all the sums of divisors up to 10000, instead of factoring each number individually, we can compute each value of $\\sigma$ in a loop, once again taking advantage of $\\sigma$ being multiplicative. (In some ways, this method is similar to the sieve of Eratosthenes - see [problem 10](https://projecteuler.net/problem=10).)"
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