What is the divisibility rule for 2?

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). 

For Example, 124 is divisible by 2 because the end digit i.e 4 is even.

How can you determine if a number is divisible by 3?

A number is divisible by 3 if the sum of its digits is divisible by 3. 
For Example, 
for the number 123, the sum is 1 + 2 + 3 = 6, which is divisible by 3. Hence, 123 is divisible by 3.

If a number n leaves a remainder of 4 when divided by 7, What can you say about n?

This means that n can be expressed in the form 
n = 7k + 4, where k is an integer. 
For Example, if k = 2, then n = 7 x 2 + 4 = 18, 
which gives a remainder of 4 when divided by 7.

Determine the remainder when 145 is divided by 6?

To find the remainder, perform the division: 
145 ÷ 6 = 24 R1. 
Thus, the remainder is 1.

Is 108 divisible by 4? Explain your reasoning.

Yes, a number is divisible by 4 if the number formed by its last two digits is divisible by 4. The last two digits of 108 are 08 
since 08 ÷ 4 = 2, 
108 is divisible by 4.

What is the divisibility rule for 5?

A number is divisible by 5 if its last digit is 0 or 5. For Example, 

235 is divisible by 5 because it ends in 5.

How do you find the remainder of 37 divided by 5?

Perform the division: 
37 ÷ 5 = 7 R2. 
The remainder is 2.

If a number is divisible by both 2 and 3, what can you conclude?

The number is divisible by 6, as 6 is the Least Common Multiple of 2 and 3.

Determine the divisibility of 144 by 8.

A number is divisible by 8 if the last three digits form a number that is divisible by 8. 
144 is divisible by 8 since 144 ÷ 8 = 18.

What is the remainder when 67 is divided by 4?

67 ÷ 4 = 16 R 3. 
Thus, the remainder is 3.

How can you check if a number is divisible by 9?

A number is divisible by 9 if the sum of its digits is divisible by 9. 
For Example, 
In 729, 7 + 2 + 9 = 18, which is divisible by 9.

If x = 10k + 3 for some integer k, 
What is the remainder when x is divided by 10?

The remainder is 3,
As x is in the form of 

10k + 3, which leaves a remainder of 3 when divided by 10.

What is the divisibility rule for 11?

A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is either 0 or divisible by 11.

Find the remainder when 225 is divided by 7.

225 ÷ 7 = 32 R1. 
Thus, the remainder is 1.

If a number is of the form 15n + 6, what can you say about its divisibility by 3?

The number is divisible by 3 since 15n is divisible by 3, and 6 is also divisible by 3.