Let N = 343,463,270. What is the ratio of the sum of the odd divisors of N to the sum of the even divisors of N?

The ratio of the sum of odd divisors to the sum of even divisors is 0.5.

Expert Answers

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For the number given N = 343,463,270. First we need to find the odd and even divisors.

First, determine the prime factorization of N.

343,463,270 = 34,346,327 × 10 = 2 × 5 × 34,346,327 = 2 × 5 × 1,733 × 19,819.

From the prime factorization of N, the even divisors are

2

2 × 5= 10

2 × 1,733= 3,466

2 × 19,819 = 39,638

2 × 5 × 1,733 = 17,330

2 × 5 × 19,819 = 198,190

2 × 1,733 × 19,819 = 68,692,654

2 × 5 × 1,733 × 19,819 = 343,463,270.

The odd divisors are

1

5

1,733

19,819

5 × 1,733 = 8,665

5 × 19,819 = 99,095

1,733 × 19,819 = 34,346,327

5 × 1,733 × 19,819 = 171,731,635.

The sum of the even divisors is 412,414,560.

The sum of the odd divisors is 206,207,280.

The ratio of 206,207,280 and 412,414,560 is 0.5

The ratio of the sum of odd divisors to the sum of even divisors is 0.5

Last Updated by eNotes Editorial on
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