Multiples of 3 and 5

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Multiples of 3 and 5

Question

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

思路

  • 暴力列举所有包含3，5因子的数，进行求和
  • 1000以内以3，5为因子的数的和，即考虑能被3，5各自整除的数的和，再去除能被15整除的数即可。

Python 代码

暴力列举法

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def sum_of_multiples1(n):
    all_sum = 0
    for i in range(1, n):
        if i%3 == 0:
            all_sum += i
        elif i%5 == 0:
            all_sum += i
    return all_sum

sum_of_multiples1(1000)
233168

公式法

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def sum_of_multiples(n):
    third_count = (n-1) // 3
    five_count = (n-1) // 5
    fifteen_count = (n-1) // 15
    print(third_count, five_count, fifteen_count)
    all_sum = 3 * (third_count)*(1+third_count)/2 + 5 * (five_count)*(1+five_count)/2 \
    - 15 * (fifteen_count)*(1+fifteen_count)/2  
    return int(all_sum)

sum_of_multiples(1000)
333 199 66





233168