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.

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.

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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.

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 (2024), 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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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

6 Questions

Q1.
Which of the following sets of numbers are divisible by 4?
Correct answer: 374 $$\quad$$ 394 $$\quad$$ 473 $$\quad$$ 848
434 $$\quad$$ 398 $$\quad$$ 247 $$\quad$$ 950
548 $$\quad$$ 343 $$\quad$$ 840 $$\quad$$ 234
Q2.
Which of the following sets of numbers are divisible by 8?
Correct answer: 374 $$\quad$$ 394 $$\quad$$ 473 $$\quad$$ 848
434 $$\quad$$ 398 $$\quad$$ 247 $$\quad$$ 950
483 $$\quad$$ 413 $$\quad$$ 840 $$\quad$$ 234
Q3.
Which of the following sets of numbers are divisible by both 4 and 8?
12 $$\quad$$ 451 $$\quad$$ 394
34 $$\quad$$ 567 $$\quad$$ 324
34 $$\quad$$ 804 $$\quad$$ 830 $$\quad$$ 484
Correct answer: 43 $$\quad$$ 294 $$\quad$$ 803 $$\quad$$ 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.