S1Q1 · Check if Either of Two Numbers is a Multiple of the Other¶

⚡ Quick Reference

Function: is_multiple(a: int, b: int) -> bool

Core idea: check if a % b == 0 or b % a == 0.

def is_multiple(a: int, b: int) -> bool:
    return a % b == 0 or b % a == 0

Key rules: - a % b == 0 → a is a multiple of b - b % a == 0 → b is a multiple of a - Either condition makes the result True

Problem Statement¶

Problem

Write a function is_multiple(a, b) that returns True if either a is a multiple of b or b is a multiple of a.

Examples:

Input

a=10, b=5

Output

True

Input

a=6, b=18

Output

True

Input

a=7, b=3

Output

False

Input

a=8, b=16

Output

True

Tracing all examples¶

`a`	`b`	`a % b`	`b % a`	Either 0?	Result
10	5	0 ✅	5%10=5	✅	`True`
6	18	6%18=6	18%6=0 ✅	✅	`True`
7	3	7%3=1	3%7=3	❌	`False`
8	16	8%16=8	16%8=0 ✅	✅	`True`

Solution approaches¶

Pythonic (direct return)ExplanatoryUsing any()Using lambda

def is_multiple(a: int, b: int) -> bool:
    return a % b == 0 or b % a == 0

def is_multiple(a: int, b: int) -> bool:
    a_is_multiple_of_b = a % b == 0
    b_is_multiple_of_a = b % a == 0
    return a_is_multiple_of_b or b_is_multiple_of_a

def is_multiple(a: int, b: int) -> bool:
    return any(x % y == 0 for x, y in [(a, b), (b, a)])

is_multiple = lambda a, b: a % b == 0 or b % a == 0

Key takeaways¶

01

x % y == 0 means x is a multiple of y

If x divided by y leaves no remainder, then x is a multiple of y. Check both directions - a % b and b % a - to cover either case.

02

Short-circuit or - stops at first True

a % b == 0 or b % a == 0 - if the first condition is already True, Python skips evaluating the second. Efficient and clean.

03

Symmetric relationship

The result is the same regardless of argument order - is_multiple(10, 5) and is_multiple(5, 10) both return True. The or of both directions ensures this symmetry.