S1Q1 · Check If a Number Divides Two Other Numbers¶

⚡ Quick Reference

Function: is_both_divisible_by(a: int, b: int, c: int) -> bool

Core idea: check if c divides both a and b using the modulo operator.

def is_both_divisible_by(a: int, b: int, c: int) -> bool:
    return a % c == 0 and b % c == 0

Key rules: - x % c == 0 means c divides x exactly - Both conditions must hold - use and - c is guaranteed non-zero - no guard needed

Problem Statement¶

Problem

Write a function is_both_divisible_by(a, b, c) that returns True if both a and b are divisible by c.

Examples:

Input

a=10, b=15, c=5

Output

True

Input

a=10, b=13, c=5

Output

False

Input

a=19, b=15, c=5

Output

False

Tracing all examples¶

`a`	`b`	`c`	`a % c`	`b % c`	Result
10	15	5	0 ✅	0 ✅	`True`
10	13	5	0 ✅	3 ❌	`False`
19	15	5	4 ❌	0 ✅	`False`

Solution approaches¶

Pythonic (direct return)ExplanatoryUsing all()Using lambda

def is_both_divisible_by(a: int, b: int, c: int) -> bool:
    return a % c == 0 and b % c == 0

def is_both_divisible_by(a: int, b: int, c: int) -> bool:
    a_divisible = a % c == 0
    b_divisible = b % c == 0
    return a_divisible and b_divisible

def is_both_divisible_by(a: int, b: int, c: int) -> bool:
    return all(n % c == 0 for n in (a, b))

Scales naturally if the problem were extended to more numbers.

is_both_divisible_by = lambda a, b, c: a % c == 0 and b % c == 0

Key takeaways¶

01

x % c == 0 is the divisibility test

The modulo operator gives the remainder. A remainder of 0 means c divides x exactly. This is the standard Python divisibility check.

02

Short-circuit and - skip second check if first fails

a % c == 0 and b % c == 0 - if a is not divisible by c, Python skips checking b entirely. The result is already False.

03

all() for extensibility

all(n % c == 0 for n in (a, b)) generalises naturally - add more numbers to the tuple without changing the logic. Good habit when checking the same condition across multiple values.