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Lesson 7 of 19
  • Year 7

Divisibility tests for 4 and 8

I can identify and explain whether a number is or is not a multiple of a given integer.

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View unit
Lesson 7 of 19
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New
  • Year 7

Divisibility tests for 4 and 8

I can identify and explain whether a number is or is not a multiple of a given integer.

Download all

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Lesson details

Key learning points

  1. A number is a multiple of 4 if and only if the last two digits are a multiple of 4.
  2. Any multiple of 4 is also a multiple of 2.
  3. A number is a multiple of 8 if and only if the last three digits are a multiple of 8.
  4. Any multiple of 8 is also a multiple of 4 and 2.

Keywords

  • Divisibility - Divisibility is a number’s ability to be exactly divided by another number, leaving no remainder.

Common misconception

Often students only consider the last 2 digits of a number to check for divisibility for 8.

The last 2 digits check for divisibility for 4 not 8.


To help you plan your year 7 maths lesson on: Divisibility tests for 4 and 8, download all teaching resources for free and adapt to suit your pupils' needs...

When talking about multiples of 4, go around the class and challenge the students to give a multiple of 4 greater than the previous person.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
List the first five multiples of 4

1, 4, 8, 12, 16
Correct answer: 4, 8, 12, 16, 20
1, 2, 4
5, 10, 15, 20
8, 12, 16, 20, 24

Q2.
List the first five multiples of 8

1, 2, 4 and 8
1, 2, 3, 4 and 5
16, 24, 32, 40, 48
Correct answer: 8, 16, 24, 32, 40
1, 8, 16, 24, 32

Q3.
Which of the following numbers are divisible by 2?

2445
5435
Correct answer: 6 578 434
46 573 567
Correct answer: 34 324 545 353 450

Q4.
Which of the following numbers are divisible by 5?

Correct answer: 327 945
820 948
400 001
555 559
Correct answer: 624 080

Q5.
Which of the following numbers are divisible by 10?

3467
4324
Correct answer: 8780
615 743
Correct answer: 756 740

Q6.
Numbers that are divisible by 3, 5 and 10 are also divisible by 1 and

Correct Answer: 30, thirty

Assessment exit quiz

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6 Questions

Q1.
Which of the following sets of numbers are divisible by 4?

374 $$\quad$$ 394 $$\quad$$ 473 $$\quad$$ 848
434 $$\quad$$ 398 $$\quad$$ 247 $$\quad$$ 950
Correct answer: 548 $$\quad$$ 344 $$\quad$$ 840 $$\quad$$ 236

Q2.
Which of the following sets of numbers are divisible by 8?

Correct answer: 376 $$\quad$$ 392 $$\quad$$ 472 $$\quad$$ 848
434 $$\quad$$ 398 $$\quad$$ 248 $$\quad$$ 950
482 $$\quad$$ 413 $$\quad$$ 840 $$\quad$$ 234

Q3.
Which of the following sets of numbers are divisible by both 4 and 8?

12 $$\quad$$ 450 $$\quad$$ 394
34 $$\quad$$ 564 $$\quad$$ 324
40 $$\quad$$ 804 $$\quad$$ 830 $$\quad$$ 484
Correct answer: 48 $$\quad$$ 296 $$\quad$$ 896 $$\quad$$ 488

Q4.
Match each set of multiples to its correct description.

Correct Answer:For all multiples of 2 ...,the digit in the ones column is a 0, 2, 4, 6 or 8

the digit in the ones column is a 0, 2, 4, 6 or 8

Correct Answer:For all multiples of 4 ...,the last two digits are a multiple of 4

the last two digits are a multiple of 4

Correct Answer:For all multiples of 8 ...,the last three digits are a multiple of 8

the last three digits are a multiple of 8

Correct Answer:For all multiples of 9 ...,the sum of the digits are a multiple of 9

the sum of the digits are a multiple of 9

Correct Answer:For all multiples of 10 ...,the digit in the ones column is a 0

the digit in the ones column is a 0

Q5.
Select the correct statement.

Jun says, “All common multiples of 4 and 8 are in the 32 times table.”
Sofia says, “All multiples of 4 are in the 8 times table.”
Aisha says, "All common multiples of 4 and 5 are odd."
Correct answer: Sam says, "All common multiples of 2, 4 and 8 are in the 8 times table."

Q6.
Jun is given 483, 783, 839, 983 and 893 and says it is not necessary to do a divisibility test for 4 or 8. Which statement explains his reasoning?

Very large numbers are unlikely to be divisible by 4 and 8
The number is prime.
Correct answer: The number is odd.
The number is even.