# 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.