here are the tricks for using the divisibility rules for
numbers 2 to 15, followed by an example for each:
Divisibility by 2: A number is divisible by 2 if its last
digit is even (0, 2, 4, 6, or 8). For example, 4856 is divisible by 2 because
its last digit, 6, is even.
Divisibility by 3: A number is divisible by 3 if the sum of
its digits is divisible by 3. For example, 4812 is divisible by 3 because 4 + 8
+ 1 + 2 = 15, which is divisible by 3.
Divisibility by 4: A number is divisible by 4 if the number
formed by its last two digits is divisible by 4. For example, 6472 is divisible
by 4 because the number formed by its last two digits, 72, is divisible by 4.
Divisibility by 5: A number is divisible by 5 if its last
digit is 0 or 5. For example, 3050 is divisible by 5 because its last digit is
0.
Divisibility by 6: A number is divisible by 6 if it is
divisible by both 2 and 3. For example, 864 is divisible by 6 because it is
divisible by both 2 and 3.
Divisibility by 7: To check for divisibility by 7, take the
last digit of the number, double it, and subtract it from the remaining digits.
If the resulting number is divisible by 7, then the original number is also
divisible by 7. For example, 378 is divisible by 7 because 37 - 2*8 = 21, which
is divisible by 7.
Divisibility by 8: A number is divisible by 8 if the number
formed by its last three digits is divisible by 8. For example, 8240 is
divisible by 8 because the number formed by its last three digits, 240, is
divisible by 8.
Divisibility by 9: A number is divisible by 9 if the sum of
its digits is divisible by 9. For example, 324 is divisible by 9 because 3 + 2
+ 4 = 9, which is divisible by 9.
Divisibility by 10: A number is divisible by 10 if its last
digit is 0. For example, 270 is divisible by 10 because its last digit is 0.
Divisibility by 11: To check for divisibility by 11, take
the alternating sum of the digits (starting with the first digit), and if the
resulting number is divisible by 11, then the original number is also divisible
by 11. For example, 3080 is divisible by 11 because 3 - 0 + 8 - 0 = 11, which
is divisible by 11.
Divisibility by 12: A number is divisible by 12 if it is
divisible by both 3 and 4. For example, 816 is divisible by 12 because it is
divisible by both 3 and 4.
Divisibility by 13: To check for divisibility by 13, take
the last digit of the number, multiply it by 4, and add this to the remaining
digits. If the resulting number is divisible by 13, then the original number is
also divisible by 13.
Example: Is 3896 divisible by 13? Yes, because when we take
the last digit (6), multiply it by 4 (6 x 4 = 24), and add it to the remaining
digits (389 + 24 = 413), the resulting number (413) is divisible by 13.
Divisibility by 14: A number is divisible by 14 if it is
divisible by both 2 and 7.
Example: Is 1344 divisible by 14? Yes, because it is
divisible by both 2 (its last digit is even) and 7 (we can apply the
divisibility rule for 7).
Divisibility by 15: A number is divisible by 15 if it is
divisible by both 3 and 5.
Example: Is 975 divisible by 15? Yes, because it is
divisible by both 3 (the sum of its digits is divisible by 3) and 5 (its last
digit is 5).
These divisibility rules and tricks can make it easier and
faster to determine whether a number is divisible by another number.
