Ruby has a rich set of built-in methods that can be used with integers. Here are some commonly used ones:

Arithmetic Methods

    num1 = 10
    num2 = 5

    # Addition
    sum = num1 + num2

    # Subtraction
    difference = num1 - num2

    # Multiplication
    product = num1 * num2

    # Division
    quotient = num1 / num2

    # Modulo (returns the remainder)
    remainder = num1 % num2

Comparison Methods

    num1 = 10
    num2 = 5

    # Equal to
    is_equal = num1 == num2

    # Not equal to
    is_not_equal = num1 != num2

    # Greater than
    is_greater_than = num1 > num2

    # Less than
    is_less_than = num1 < num2

    # Greater than or equal to
    is_greater_than_or_equal_to = num1 >= num2

    # Less than or equal to
    is_less_than_or_equal_to = num1 <= num2

Bitwise Methods

    num1 = 10
    num2 = 5

    # Bitwise AND
    result = num1 & num2

    # Bitwise OR
    result = num1 | num2

    # Bitwise XOR
    result = num1 ^ num2

    # Bitwise NOT
    result = ~num1

    # Bitwise left shift
    result = num1 << 1

    # Bitwise right shift
    result = num1 >> 1

Conversion Methods

    num = 10

    # Convert to binary
    binary = num.to_s(2)

    # Convert to octal
    octal = num.to_s(8)

    # Convert to hexadecimal
    hexadecimal = num.to_s(16)

Formatting Methods

    num = 10

    # Format as a string with leading zeros
    formatted_str = num.to_s.rjust(4, '0')

    # Format as a string with leading spaces
    formatted_str = num.to_s.rjust(4)

    # Format as a string with trailing zeros
    formatted_str = num.to_s.ljust(4, '0')

    # Format as a string with trailing spaces
    formatted_str = num.to_s.ljust(4)

Prime Number Methods

    require 'prime'

    num = 10

    # Check if the number is prime
    is_prime = Prime.prime?(num)

    # Get the next prime number
    next_prime = Prime.next_prime(num)

    # Get the previous prime number
    prev_prime = Prime.prev_prime(num)

Exponential Methods

    num = 2

    # Raise to a power
    result = num ** 3

    # Raise to a power and take the modulus
    result = num ** 3 % 5

    # Take the square root
    square_root = Math.sqrt(num)

Range Methods

    range = 1..10

    # Convert range to an array
    array = range.to_a

    # Get the maximum value in the range
    max_value = range.max

    # Get the minimum value in the range
    min_value = range.min

    # Check if a value is within the range
    within_range = range.include?(5)

Division Methods

    num1 = 10
    num2 = 3

    # Integer division
    result = num1 / num2

    # Modulus (remainder) after division
    remainder = num1 % num2

    # Float division
    result = num1.to_f / num2

Other Methods

    num = 10

    # Check if the number is even
    is_even = num.even?

    # Check if the number is odd
    is_odd = num.odd?

    # Check if the number is a perfect square
    is_square = (Math.sqrt(num) % 1 == 0)

    # Round to the nearest integer
    rounded_int = num.round

        These methods can be useful for working with ranges of numbers, performing division operations, and checking various properties of numbers such as evenness and perfect squares.