Problems
1. Sum of naturals divisible by 3 and 5
Write a program that calculates and prints the sum of all the natural numbers divisible by either 3 or 5, up to a given limit entered by the user.
2. Greatest common divisor
Write a program that, given two positive integers, will calculate and print the greatest common divisor of the two.
3. Least common multiple
Write a program that will, given two or more positive integers, calculate and print the least common multiple of them all.
4. Largest prime smaller than given number
Write a program that computes and prints the largest prime number that is smaller than a number provided by the user, which must be a positive integer.
5. Sexy prime pairs
Write a program that prints all the sexy prime pairs up to a limit entered by the user.
6. Abundant numbers
Write a program that prints all abundant numbers and their abundance, up to a number entered by the user.
7. Amicable numbers
Write a program that prints the list of all pairs of amicable numbers smaller than 1,000,000.
8. Armstrong numbers
Write a program that prints all Armstrong numbers with three digits.
9. Prime factors of a number
Write a program that prints the prime factors of a number entered by the user.
10. Gray code
Write a program that displays the normal binary representations, Gray code representations, and decoded Gray code values for all 5-bit numbers.
11. Converting numerical values to Roman
Write a program that, given a number entered by the user, prints its Roman numeral equivalent.
12. Largest Collatz sequence
Write a program that determines and prints which number up to 1 million produces the longest Collatz sequence and what its length is.
13. Computing the value of Pi
Write a program that computes the value of Pi with a precision of two decimal digits.
14. Validating ISBNs
Write a program that validates that 10-digit values entered by the user, as a string, represent valid ISBN-10 numbers.