Lesson 24

Divisibility - % in conditions

After this lesson: You'll check whether a number divides by another with no remainder, and recognise even numbers.

Video

The video for this lesson is coming soon.

Explanation

Remember % from lesson 5? It gives the remainder of a division: 14 % 3 is 2, because 14 = 4 · 3 + 2. Today we'll use it for the most important question: does something divide with no remainder? It's the key to lots of contest tasks! 🔑

Teams in PE class 🎬

Click Next - you'll see what dividing with no remainder means.

Bajtek

🧒🧒🧒🧒🧒🧒🧒🧒🧒🧒🧒🧒

Teams of three

There are 12 children in PE, and the teacher splits them into teams of 3 for 3x3 basketball. We line the children up in rows of 3...

Step 1 / 4

Will the teams be equal?

14 children in rows of 3 - watch what is left at the end.

🧒 🧒 🧒 | 🧒 🧒 🧒 | 🧒

Click the arrow - we'll lay the number out in rows and see whether anything is left.

Code

1children = 14
2if children % 3 == 0:
3    print("Equal teams!")
4else:
5    print("Someone is left without a team")

Screen

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15 children

One more child - and everything fits.

🏀1children = 15

if children % 3 == 0

3print("Equal teams!")

✅

elsein every other case

5print("Someone is left without a team")

😕

Click the arrow - I'll walk the program's path, line by line.

Code

1children = 15
2if children % 3 == 0:
3    print("Equal teams!")
4else:
5    print("Someone is left without a team")

Screen

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Even or odd?

The most common question about divisibility is: is the number even? Even = divides by 2 with no remainder:

Condition	Means
`n % 2 == 0`	n is even (2, 4, 10, 0, -6...)
`n % 2 != 0`	n is odd (1, 7, 15, -3...)

The pairs of socks 🧦 from lesson 5: an even number of socks - all of them have a pair. Odd - one is left alone.

Socks in pairs 🧦

Type a number of socks 🧦 (e.g. 7, at most 60) and press Enter ⏎ - you'll see whether every one has a pair.

🧦 🧦 🧦 | 🧦 🧦 🧦 | 🧦

Click the arrow - we'll lay the number out in rows and see whether anything is left.

Code

1socks_str = input()
2socks = int(socks_str)
3if socks % 2 == 0:
4    print("Even - every sock has a pair")
5else:
6    print("Odd - one is left alone")

Screen

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By any number you like

We check divisibility by any number the same way:

n % 5 == 0 - ends in 0 or 5 (5, 10, 35, 100...),
n % 10 == 0 - ends in 0 (a round number),
n % 7 == 0 - it's in the 7 times table (7, 14, 21...),
a % b == 0 - b is a divisor of a (e.g. 3 is a divisor of 12).

Egg boxes 🥚

A box holds 6 eggs. Type a number of eggs 🥚 (at most 60) and press Enter ⏎ - will all the boxes be full?

🥚 🥚 🥚 | 🥚 🥚 🥚 | 🥚

Click the arrow - we'll lay the number out in rows and see whether anything is left.

Code

1eggs_str = input()
2eggs = int(eggs_str)
3if eggs % 6 == 0:
4    print("All the boxes are full!")
5else:
6    print("One box isn't full")

Screen

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The Pif-Paf game 🎬

Click Next - a game where the order of the conditions is a trap.

Bajtek

3 ➡️ Pif5 ➡️ Paf15 ➡️ PifPaf

The rules

The children count in turn. Whoever gets a number divisible by 3 says Pif. Divisible by 5 - Paf. And divisible by both 3 and 5 (15, 30...) - PifPaf! Otherwise you just say the number.

Step 1 / 3

Play Pif-Paf 🎲

Type a number 🔢 (e.g. 9, 10, 30 or 7) and press Enter ⏎ - what do you have to say?

🎲1n_str = input()

2n = int(n_str)

if n % 15 == 0

4print("PifPaf")

💥

elif n % 3 == 0

6print("Pif")

🔵

elif n % 5 == 0

8print("Paf")

🟠

elsein every other case

10print(n)

🔢

Click the arrow - I'll walk the program's path, line by line.

Code

1n_str = input()
2n = int(n_str)
3if n % 15 == 0:
4    print("PifPaf")
5elif n % 3 == 0:
6    print("Pif")
7elif n % 5 == 0:
8    print("Paf")
9else:
10    print(n)

Screen

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Which condition checks whether n is odd?

What will this program print?

n = 20
if n % 6 == 0:
    print("A")
else:
    print(n % 6)

Which number should be checked first in Pif-Paf?

Remember

n % k == 0 - n divides by k with no remainder.
n % 2 == 0 - even, n % 2 != 0 - odd.
a % b == 0 means b is a divisor of a.
When conditions are inside each other (15 → 3 and 5), check the most demanding one first.

On to the tasks! Each one is a question: does something divide with no remainder?

Tasks from the video

We solve them together in the video - pause it and try first on your own.

1Divisible by 3?2Even or odd 3Equal teams 4A divisor 5Pif-Paf 6Egg boxes 7Ending in zero or five 8Every four years

Practice tasks

Try to solve them without the video. Stuck? Every task has hints and an editorial.

9Divisible by 9?10Buses for a trip 11No remainder or the remainder 12An even sum