In python a number of mathematical operations can be performed with ease by importing a module named “math” which defines various functions which makes our tasks easier.

**1. ceil()** :- This function returns the **smallest integral value greater than the number**. If number is already integer, same number is returned.

**2. floor()** :- This function returns the **greatest integral value smaller than the number**. If number is already integer, same number is returned.

`# Python code to demonstrate the working of` `# ceil() and floor()` ` ` `# importing "math" for mathematical operations` `import` `math` ` ` `a ` `=` `2.3` ` ` `# returning the ceil of 2.3` `print` `(` `"The ceil of 2.3 is : "` `, end` `=` `"")` `print` `(math.ceil(a))` ` ` `# returning the floor of 2.3` `print` `(` `"The floor of 2.3 is : "` `, end` `=` `"")` `print` `(math.floor(a))` |

Output:

The ceil of 2.3 is : 3 The floor of 2.3 is : 2

**3. fabs()** :- This function returns the **absolute value** of the number.

**4. factorial()** :- This function returns the **factorial** of the number. An error message is displayed if number is not integral.

`# Python code to demonstrate the working of` `# fabs() and factorial()` ` ` `# importing "math" for mathematical operations` `import` `math` ` ` `a ` `=` `-` `10` ` ` `b` `=` `5` ` ` `# returning the absolute value.` `print` `(` `"The absolute value of -10 is : "` `, end` `=` `"")` `print` `(math.fabs(a))` ` ` `# returning the factorial of 5` `print` `(` `"The factorial of 5 is : "` `, end` `=` `"")` `print` `(math.factorial(b))` |

Output:

The absolute value of -10 is : 10.0 The factorial of 5 is : 120

**5. copysign(a, b)** :- This function returns the number with the **value of ‘a’ but with the sign of ‘b’**. The returned value is float type.

**6. gcd() **:- This function is used to compute the **greatest common divisor of 2 numbers** mentioned in its arguments. This function works in python 3.5 and above.

`# Python code to demonstrate the working of` `# copysign() and gcd()` ` ` `# importing "math" for mathematical operations` `import` `math` ` ` `a ` `=` `-` `10` `b ` `=` `5.5` `c ` `=` `15` `d ` `=` `5` ` ` `# returning the copysigned value.` `print` `(` `"The copysigned value of -10 and 5.5 is : "` `, end` `=` `"")` `print` `(math.copysign(` `5.5` `, ` `-` `10` `))` ` ` `# returning the gcd of 15 and 5` `print` `(` `"The gcd of 5 and 15 is : "` `, end` `=` `"")` `print` `(math.gcd(` `5` `,` `15` `))` |

Output:

The copysigned value of -10 and 5.5 is : -5.5 The gcd of 5 and 15 is : 5

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