Divisible by every factor
A block of 12 cuts into groups of each of its factors.
A number divisible by 12
A number is divisible by 12. For example 12, 24, 36, 48 …
Is it always divisible by 4 as well?
What this lesson covers
The idea
If A is divisible by k, then A is divisible by all the factors of k.
A number divisible by 12
A number is divisible by 12. For example 12, 24, 36, 48 …
Is it always divisible by 4 as well?
- Yes, always
- Only sometimes
- Never
Cut a block of 12
A is made of blocks of 12. Tap a number to cut every block into groups of that size. Which numbers leave nothing over?
A factor of a factor
If A is divisible by k, then A is divisible by all the factors of k.
A = 12m. And 12m = 2 × 6 × m = 3 × 4 × m. So A is divisible by 2, 6, 3 and 4. A block of 12 splits into groups of each factor, so any number of blocks does.
Only the factors are certain. 8 is not a factor of 12: 24 is divisible by 8, but 36 is not.
Notes
If A is divisible by k, then A is divisible by all the factors of k.
Check yourself
A number is divisible by 18. Which number must divide it?
A number is divisible by 20. How many different numbers (including 1 and 20) must divide it?
Answer: 6
The factors of 20 are 1, 2, 4, 5, 10, 20. That is 6 numbers. All of them divide every multiple of 20.
A number is divisible by 24. Which statement is always true?
A number is divisible by 60. What is the largest number below 60 that must divide it?
Answer: 30
The factors of 60 below 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30. The largest is 30.
- 4. 4 is not a factor of 18. The number 18 itself is divisible by 18 but not by 4.
- 6 — correct. Yes! 6 is a factor of 18 (18 = 6 × 3), so it must divide every number divisible by 18.
- 12. 12 is not a factor of 18. The number 18 itself is not divisible by 12.
- 36. 36 is bigger than 18, not a factor of it. The number 18 itself is not divisible by 36.
- It is divisible by 5. 5 is not a factor of 24. The number 24 itself is not divisible by 5.
- It is divisible by 8 and by 12 — correct. Yes! 8 and 12 are both factors of 24 (24 = 8 × 3 = 12 × 2).
- It is divisible by 16. 16 is not a factor of 24. The number 24 itself is not divisible by 16.
- It is divisible by 48. 48 is bigger than 24. The number 24 itself is not divisible by 48.