New
New
Divisibility tests for 4 and 8
I can identify and explain whether a number is or is not a multiple of a given integer.
Lesson 7 of 19
New
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.
Lesson details
Key learning points
- A number is a multiple of 4 if and only if the last two digits are a multiple of 4.
- Any multiple of 4 is also a multiple of 2.
- A number is a multiple of 8 if and only if the last three digits are a multiple of 8.
- 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.
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 (2026), 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
6 Questions
Q1.List the first five multiples of 4
List the first five multiples of 4
1, 4, 8, 12, 16
Correct answer: 4, 8, 12, 16, 20
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
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
8, 16, 24, 32, 40
1, 8, 16, 24, 32
Q3.Which of the following numbers are divisible by 2?
Which of the following numbers are divisible by 2?
2445
5435
Correct answer: 6 578 434
6 578 434
46 573 567
Correct answer: 34 324 545 353 450
34 324 545 353 450
Q4.Which of the following numbers are divisible by 5?
Which of the following numbers are divisible by 5?
Correct answer: 327 945
327 945
820 948
400 001
555 559
Correct answer: 624 080
624 080
Q5.Which of the following numbers are divisible by 10?
Which of the following numbers are divisible by 10?
3467
4324
Correct answer: 8780
8780
615 743
Correct answer: 756 740
756 740
Q6.Numbers that are divisible by 3, 5 and 10 are also divisible by 1 and
Numbers that are divisible by 3, 5 and 10 are also divisible by 1 and
Correct Answer: 30, thirty
30, thirty
Assessment exit quiz
6 Questions
Q1.Which of the following sets of numbers are divisible by 4?
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
548 $$\quad$$ 344 $$\quad$$ 840 $$\quad$$ 236
Q2.Which of the following sets of numbers are divisible by 8?
Which of the following sets of numbers are divisible by 8?
Correct answer: 376 $$\quad$$ 392 $$\quad$$ 472 $$\quad$$ 848
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?
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
48 $$\quad$$ 296 $$\quad$$ 896 $$\quad$$ 488
Q4.Match each set of multiples to its correct description.
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
For all multiples of 2 ... - 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
For all multiples 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
For all multiples 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
For all multiples 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
For all multiples of 10 ... - the digit in the ones column is a 0
Q5.Select the correct statement.
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."
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?
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 odd.
The number is even.
