Let N = 34,463,270. What is the ratio of the sum of the odd divisors of N to the sum of the even divisors of N?

For the number 343,463,270, the ratio of the sum of odd divisors and the sum of the even divisors is 0.5.

Expert Answers

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The prime factorization of the number N = 343,463,270 is 2 x 5 x 1,733 x 19,819.

This can be used to determine the odd and even divisors.

The even divisors of the number N are 2, 10, 3,466, 17,330, 39,638, 198,190, 68,692,654, 343,463,270.

The odd divisors of the number N are 1, 5, 1,733, 8,665, 19,819, 99,095, 34,346,327, 171,731,635.

Adding the even divisors of N gives the sum as 412,414,560, and adding the odd divisors gives their sum as 206,207,280.

Dividing the sum of the odd divisors by the sum of the even divisors gives their ratio R = 206,207,280/412,414,560 = 0.5.

The required ratio of the sum of the odd divisors and the sum of the even divisors is 0.5.

Last Updated by eNotes Editorial on
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