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
Is this number divisible by 4?
36,984
Yes
The last two digits are 84
84 is divisible by 4
Is this number divisible by 5?
1,743,560
Yes
The last digit is a 0
Is this number divisible by 9?
237,924
Yes
2 + 3 + 7 + 9 + 2 + 4 = 27
27 is divisible by 9
Is this number divisible by 9?
3,503,617
No
3 + 5 + 0 + 3 + 6 + 1 + 7 = 25
25 is not divisible by 9
Is this number divisible by 3?
5,905
No
5 + 9 + 0 + 5 = 19
19 is not divisible by 3
Is this number divisible by 8?
725,911
No
The hundreds digit is odd, so we add 4 to the last two digits
11 + 4 = 15
15 is not divisible by 8
Is this number divisible by 11?
88,880
Yes
8 - 8 + 8 - 8 + 0 = 0
0 is divisible by 11
Is this number divisible by 6?
801,302
No
Even though it is divisible by 2 (even)
It is not divisible by 3
(8+0+1+3+0+2=14 which is not divisible by 3)
Is this number divisible by 9?
8,924
No
8 + 9 + 2 + 4 = 23
23 is not divisible by 9
Is this number divisible by 7?
703
No
Double the last digit = 2x3 = 6
Take it away from the rest of the number: 70 - 6 = 64
64 is not divisible by 7
Is this number divisible by 6?
72,804
Yes
It is divisible by 2 (even)
AND
It is divisible by 3
(7+2+8+0+4=21 which is divisible by 3)
Is this number divisible by 10?
2,714
No
It doesn’t end in a 0
Is this number divisible by 12?
111,111
No
Even though it is divisible by 3 (1+1+1+1+1+1=6)
It is not divisible by 4:
last two digits = 11, which is not divisble by 4
Is this number divisible by 4?
3,374
No
The last two digits are 74
74 is not divisible by 4
Is this number divisible by 3?
4593
Yes
4 + 5 + 9 + 3 = 21
21 is divisible by 3
Is this number divisible by 12?
46,444
No
It is not divisible by 3:
4+6+4+4+4=22, which is not divisible by 3
Is this number divisible by 2?
1,803,456
Yes, it ends in an even number.
Is this number divisible by 6?
31,496
No
Even though it is divisible by 2 (even)
It is not divisible by 3
(3+1+4+9+6=23 which is not divisible by 3)
Is this number divisible by 12?
46,944
Yes
It is divisible by 3: 4+6+9+4+4=27, which is divisible by 3
It is divisible by 4: last two digits = 44, which is divisble by 4
Is this number divisible by 8?
806
No
The hundreds digit is even, so we look at the last two digits
6 is not divisible by 8
Is this number divisible by 10?
88,888
No
It doesn’t end in a 0
Is this number divisible by 6?
666
Yes
It is divisible by 2 (even)
AND
It is divisible by 3
(6+6+6=18 which is divisible by 3)
Is this number divisible by 11?
142,714
Yes
1 - 4 + 2 - 7 + 1 - 4 = -11
-11 is divisible by 11
Is this number divisible by 2?
693
No, it doesn’t end in an even number.
Is this number divisible by 6?
1,801,307
No
It is not divisible by 2 (odd)
Is this number divisible by 7?
450
No
Double the last digit = 2x0 = 0
Take it away from the rest of the number: 45 - 0 = 45
45 is not divisible by 7
Is this number divisible by 10?
57,240
Yes
It ends in a 0
Is this number divisible by 11?
142,712
No
1 - 4 + 2 - 7 + 1 - 2 = -9
-9 is not divisible by 11
Is this number divisible by 5?
34,287
No
The last digit is not a 0 or 5
Is this number divisible by 12?
924
Yes
It is divisible by 3: 9+2+4=15, which is divisible by 3
It is divisible by 4: last two digits = 24, which is divisble by 4
Is this number divisible by 9?
3,503,610
Yes
3 + 5 + 0 + 3 + 6 + 1 + 0 = 18
18 is divisible by 9
Is this number divisible by 5?
97,435
Yes
The last digit is a 5
Is this number divisible by 11?
679,459
Yes
6 - 7 + 9 - 4 + 5 - 9 = 0
0 is divisible by 11
Is this number divisible by 10?
768,139,619
No
It doesn’t end in a 0
Is this number divisible by 3?
41,502
Yes
4 + 1 + 5 + 0 + 2 = 12
12 is divisible by 3
Is this number divisible by 2?
3,459,853
No, it doesn’t end in an even number.
Is this number divisible by 3?
1,652,004
Yes
1 + 6 + 5 + 2 + 0 + 0 + 4 = 18
18 is divisible by 3
Is this number divisible by 4?
1,652,004
Yes
The last two digits are 04
4 is divisible by 4
Is this number divisible by 8?
725,912
Yes
The hundreds digit is odd, so we add 4 to the last two digits
12 + 4 = 16
16 is divisible by 8
Is this number divisible by 4?
1,743,569
No
The last two digits are 69
69 is not divisible by 4
Is this number divisible by 7?
672
Yes
Double the last digit = 2x2 = 4
Take it away from the rest of the number: 67 - 4 = 63
63 is divisible by 7
Is this number divisible by 10?
1,949,400
Yes
It ends in a 0
Is this number divisible by 6?
1,801,302
Yes
It is divisible by 2 (even)
AND
It is divisible by 3
(1+8+0+1+3+0+2=15 which is divisible by 3)
Is this number divisible by 2?
31,428
Yes, it ends in an even number.
Is this number divisible by 7?
833
Yes
Double the last digit = 2x3 = 6
Take it away from the rest of the number: 83 - 6 = 77
77 is divisible by 7
Is this number divisible by 12?
2,892
Yes
It is divisible by 3: 2+8+9+2=21, which is divisible by 3
It is divisible by 4: last two digits = 92, which is divisble by 4
Is this number divisible by 8?
55,628
No
The hundreds digit is even, so we look at the last two digits
28 is not divisible by 8
Is this number divisible by 2?
4592
Yes, it ends in an even number.
Is this number divisible by 12?
5,678
No
It is not divisible by 3:
5+6+7+8=26, which is not divisible by 3
Is this number divisible by 4?
1,743,560
Yes
The last two digits are 60
60 is divisible by 4
Is this number divisible by 3?
674
No
6 + 7 + 4 = 17
17 is not divisible by 3
Is this number divisible by 7?
364
Yes
Double the last digit = 2x4 = 8
Take it away from the rest of the number: 36 - 8 = 28
28 is divisible by 7
Is this number divisible by 8?
1680
Yes
The hundreds digit is even, so we look at the last two digits
80 is divisible by 8
Is this number divisible by 2?
15,867
No, it doesn’t end in an even number.
Is this number divisible by 5?
82,174
No
The last digit is not a 0 or 5