Project Euler Problem (1~10)

1.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 100

(计算1000以内能被3或5整除的数之和)

#include <iostream>
using namespace std;
int main()
{
	int i;
	int sum = 0;
	for (i = 1; i <= 1000; i++)
	{
		if (i % 3 == 0 || i % 5 == 0)
			sum = sum + i;
	}
	cout << sum << endl;
	return 0;
}

运行结果：

234168

2.Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...Find the sum of all the even-valued terms in the sequence which do not exceed one million.

（计算斐波那契数列中小于100万的偶数项之和）

#include <iostream>
using namespace std;
int main()
{
	int a = 1, b = 2;
	int sum = 0;
	while(a < 1000000 && b < 1000000)
	{
		if (a % 2 == 0)
			sum = sum + a;
		if (b % 2 == 0)
			sum = sum + b;
		a = a + b;
		b = b + a;
	}
	cout << sum << endl;
	return 0;
}

运行结果：

257114

3.The prime factors of 13195 are 5, 7, 13 and 29.What is the largest prime factor of the number 317584931803?

(分解出317584931803的因数）

#include <iostream>
using namespace std;
int main()
{
	int i;
	long long n = 317584931803;
	for (i = 2; i <= n; i++)
	{
		while (n != i)
		{
			if (n % i == 0)
			{
				n = n / i;
			}
			else
				break;
		}
	} //从2开始将每个数作为n的除数，若整除则为因数后重新计算n再判断
	cout << n << endl;//前面只输入前面几个较小因数，重新计算的最后一个n为最大因数
	return 0;
}

运行结果：

3919

4.A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 99.Find the largest palindrome made from the product of two 3-digit numbers.

(找出两个三位数相乘的最大回文数）