Hope this helps
Brainlest please?
Step-by-step explanation:
1
Any integer (not a fraction) is divisible by 1
2
The last digit is even (0,2,4,6,8)
128 Â Yes
129 Â No
3
The sum of the digits is divisible by 3
381 (3+8+1=12, and 12á3 = 4) Yes
217 (2+1+7=10, and 10á3 = 3 1/3) No
This rule can be repeated when needed:
99996 (9+9+9+9+6 = 42, then 4+2=6) Yes
4
The last 2 digits are divisible by 4
1312 is (12á4=3) Yes
7019 is not (19á4=4 3/4) No
A quick check (useful for small numbers) is to halve the number twice and the result is still a whole number.
12/2 = 6, 6/2 = 3, 3 is a whole number. Yes
30/2 = 15, 15/2 = 7.5 which is not a whole number. No
5
The last digit is 0 or 5
175 Â Yes
809 Â No
6
Is even and is divisible by 3 (it passes both the 2 rule and 3 rule above)
114 (it is even, and 1+1+4=6 and 6á3 = 2) Yes
308 (it is even, but 3+0+8=11 and 11á3 = 3 2/3) No
7
Double the last digit and subtract it from a number made by the other digits. The result must be divisible by 7. (We can apply this rule to that answer again)
672 (Double 2 is 4, 67â4=63, and 63á7=9) Yes
105 (Double 5 is 10, 10â10=0, and 0 is divisible by 7) Yes
905 (Double 5 is 10, 90â10=80, and 80á7=11 3/7) No
8
The last three digits are divisible by 8
109816 (816á8=102) Yes
216302 (302á8=37 3/4) No
A quick check is to halve three times and the result is still a whole number:
816/2 = 408, 408/2 = 204, 204/2 = 102 Yes
302/2 = 151, 151/2 = 75.5 No
9
The sum of the digits is divisible by 9
(Note: This rule can be repeated when needed)
1629 (1+6+2+9=18, and again, 1+8=9) Yes
2013 (2+0+1+3=6) No
10
The number ends in 0
220 Â Yes
221 Â No
11
Add and subtract digits in an alternating pattern (add digit, subtract next digit, add next digit, etc). Then check if that answer is divisible by 11.
1364 (+1â3+6â4 = 0) Yes
913 (+9â1+3 = 11) Yes
3729 (+3â7+2â9 = â11) Yes
987 (+9â8+7 = 8) No
12
The number is divisible by both 3 and 4 (it passes both the 3 rule and 4 rule above)
648
(By 3? 6+4+8=18 and 18á3=6 Yes)
(By 4? 48á4=12 Yes)
Both pass, so Yes
524
(By 3? 5+2+4=11, 11á3= 3 2/3 No)
(Don't need to check by 4) No