Rules Of Divisibility

Question 1

9

Answer 1

Sum of digits divisible by 9

Question 2

Divisible by 4

Answer 2

Last 2 digits divisible by 4

Question 3

Divisible by 8

Answer 3

Last digits make up number divisible by 8

Eg 5816

Question 4

6

Answer 4

Divisible by 2 and 3 - i.e. An even number who’s digits add up to a multiple of 3.

Question 5

11

Answer 5

Sum of digits in odd places - sum of digits in even places = a number divisible by 11

Eg - 121792

1st, 3rd, and 5th places (odd) is 1+1+9 = 11
2nd, 4th and 6th places (even) is 2+7+2 = 11
11-11=0 , which is divisible by 11.

Question 6

3

Answer 6

Sum of digits divisible by 3

Question 7

7

Answer 7

1) Multiply the number of hundreds the number has by 2
2) Add the remaining two digits
3) If the result is divisible by 7, the number is divisible by 7

Question 8

What is the general rule of divisibility and prime factors?

Answer 8

An integer n is divisible by smaller integer g if n is divisible by all of g’s prime factors.

Question 9

When testing divisibility using larger building blocks that are not prime, what should you remember?

Answer 9

Use building blocks that have no common divisor greater than 1.

Question 10

When calculating how many factors a number has, while using a factor chart, when should you stop? Note that you are calculating the number of factors - not the factors themselves.

Answer 10

Stop at the square root of the number. Basically, where the numbers square to a perfect square at the number.