Maths Ext 1. Divisibility rules Flashcards
How do you check if a number is divisible by 2?
- Look at the last (units) digit of the number.
- If it is even (i.e. a 0, 2, 4, 6 or 8), then the whole number is divisible by 2
How do you check if a number is divisible by 3?
- Add up all the digits
- Check if this answer is divisible by 3. If it is, so is the original number
- (If you’re not sure, add up all the digits of the second number and check again to see if the result is divisible by 3)
How do you check if a number is divisible by 4?
- Look at the last two digits (tens and units)
- If this is divisible by 4, then so is the original number
How do you check if a number is divisible by 5?
- Look at the last digit
- If this is a 0 or a 5, then the whole number is divisible by 5
How do you check if a number is divisible by 6?
For a number to be divisible by 6, it needs to pass the rules for divisibility by 2 and divisibility by 3:
- Check if the number is divisible by 2
- Check if the number is divisible by 3
- If these both work, then the number is divisible by 6
How do you check if a number is divisible by 7?
- Split the number by removing the last digit
- Double the last digit. Let’s call the answer A.
- Take A away from whatever is left of your original number after you removed the last digit
- If the answer is divisible by 7, then so is the original number
How do you check if a number is divisible by 8?
- Look at the hundreds digit
- If the hundred digit is even: the last two digits must be divisible by 8.
- If the hundreds digit is odd: add 4 to the last two digits. This must be divisible by 8.
How do you check if a number is divisible by 9?
- Add up all the digits
- Check if this answer is divisible by 9. If it is, so is the original number
- (If you’re not sure, add up all the digits of the second number and check again to see if the result is divisible by 9)
How do you check if a number is divisible by 10?
- Look at the last digit
- If it is a 0, then the original number is divisible by 10
How do you check if a number is divisible by 11?
- Add and subtract the digits of the number in an alternating pattern
- If the answer is divisible by 11, so is the original number
How do you check if a number is divisible by 12?
For a number to be divisible by 12, it needs to pass the rules for divisibility by 3 and divisibility by 4:
- Check if the number is divisible by 3
- Check if the number is divisible by 4
- If these both work, then the number is divisible by 12
Is this number divisible by 3?
32,593
No
3 + 2 + 5 + 9 + 3 = 22
22 is not divisible by 3
Is this number divisible by 5?
846,202
No
The last digit is not a 0 or 5
Is this number divisible by 7?
171
No
Double the last digit = 2x1 = 2
Take it away from the rest of the number: 17 - 2 = 15
15 is not divisible by 7
Is this number divisible by 9?
57,245
No
7 + 5 + 2 + 4 + 5 = 23
23 is not divisible by 9
Is this number divisible by 8?
71,587
No
The hundreds digit is odd, so we add 4 to the last two digits
87 + 4 = 91
91 is not divisible by 8
Is this number divisible by 4?
248,351
No
The last two digits are 51
51 is not divisible by 4
Is this number divisible by 10?
768,139,610
Yes
It ends in a 0
Is this number divisible by 11?
90,375
No
9 - 0 + 3 - 7 + 5 = 10
10 is not divisible by 11
Is this number divisible by 8?
13,496
Yes
The hundreds digit is even, so we look at the last two digits
96 is divisible by 8
Is this number divisible by 8?
1,840,336
Yes
The hundreds digit is odd, so we add 4 to the last two digits
36 + 4 = 40
40 is divisible by 8
Is this number divisible by 5?
846,205
Yes
The last digit is a 5
Is this number divisible by 9?
1,860,336
Yes
1 + 8 + 6 + 0 + 3 + 3 + 6 = 27
27 is divisible by 9
Is this number divisible by 11?
1,408,412
No
1 - 4 + 0 - 8 + 4 - 1 + 2 = -6
-6 is not divisible by 11
