Discrete Mathematics Questions and Answers – Counting – Number and Sum of Divisors

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This set of Advanced Discrete Mathematics Questions and Answers focuses on “Counting – Number and Sum of Divisors”.

1. Calculate sum of divisors of n = 1900.
a) 6530
b) 5346
c) 3387
d) 4123
View Answer

Answer: d
Explanation: The prime factorization of 1800 is 19 * 22 * 52 and
S(22) = 1 + 2 + 4 = 7
S(52) = 1 + 5 + 25 = 31
Therefore, S(1800) = 19 * 7 * 31 = 4123.
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2. Given the factorization of a number n, then the sum of divisors can be computed in _______
a) linear time
b) polynomial time
c) O(logn)
d) o(n+1)
View Answer

Answer: b
Explanation: The exact number of running time depends on the computational model. When analyzing arithmetic with large numbers, we usually count either bit operations or arithmetic operations of size O(logn) (where n is the input size). Now, given the factorization of a number n, then the sum of divisors can be computed in polynomial time.

3. Calculate the sum of divisors of N = 9600.
a) 23250
b) 47780
c) 54298
d) 31620
View Answer

Answer: d
Explanation: The prime factorization of 1800 is 3 * 27 * 52 and
S(3) = 1 + 3 = 4
S(22) = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255
S(52) = 1 + 5 + 25 = 31
Therefore, S(1800) = 4 * 255 * 31 = 31620.

4. Find the number of odd positive integers of the number 456.
a) 54
b) 27
c) 16
d) 8
View Answer

Answer: d
Explanation: To find the number of odd factors (which includes 1), we can exclude any power of 2 and do the same. So, for 456, we have (3 + 1)(1 + 1) = 8 odd positive factors.

5. The number of even positive integers of 3200 is _______
a) 24
b) 32
c) 164
d) 209
View Answer

Answer: a
Explanation: To find the number of even factors, we can multiply the number of even factors by the power of 2. For 3200, we have (5 + 1)(1 + 1)(2) = 24 even factors.
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6. What is the sum of divisors of the number 1872?
a) 12493
b) 5438
c) 45862
d) 654
View Answer

Answer: a
Explanation: The prime factorization of 1872 is 13 * 32 * 24 and S(24) = 1 + 2 + 4 + 8 + 16 = 31, S(52) = 1 + 5 + 25 = 31. Therefore, S(1872) = 31 * 31 * 13 = 12493.

7. Find the odd positive integer of the number 6500.
a) 43
b) 17
c) 12
d) 87
View Answer

Answer: c
Explanation: To find the number of odd factors, we can exclude any power of 2 and do the same. So, for 6500, we have (5 + 1)(1 + 1) = 6 * 2 = 12 odd positive factors.

8. How many even positive integers are there in the number 7362?
a) 16
b) 58
c) 35
d) 165
View Answer

Answer: a
Explanation: To find the number of even factors, we can multiply the number of even factors by the power of 2. For 5065, we have (3 + 1)(1 + 1)(2) = 4 * 2 * 2 = 16 even factors.

9. Calculate sum of divisors of n = 8620.
a) 7549
b) 54201
c) 18102
d) 654
View Answer

Answer: c
Explanation: The prime factorization of 1800 is 431 * 22 * 5 and
S(22) = 1 + 2 + 4 = 7
S(52) = 1 + 5 = 6
Therefore, S(1800) = 6 * 7 * 431 = 18102.

10. Find the odd positive integer of the number 4380.
a) 108
b) 48
c) 75
d) 8
View Answer

Answer: b
Explanation: To find the number of odd factors, we can exclude any power of 2 and do the same. So, for 6500, we have (5 + 1)(3 + 1)(1 + 1) = 6 * 4 * 2 = 48 odd positive factors.
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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn