Divisibility Rules for 2, 4 and 10 - Examples, Exercises and Solutions

To determine if the number 43 is divisible by 4, we apply the divisibility rule for 4:

• According to the rule, a number is divisible by 4 if the last two digits of the number, treated as a separate number, are divisible by 4.
• For the number 43, the last two digits are "43" itself.
• We now test if 43 is divisible by 4 by performing a simple division: $\frac{43}{4}$.

Dividing 43 by 4 gives us:

$\frac{43}{4} = 10.75$

Since 10.75 is not a whole number, 43 is not divisible by 4 without leaving a remainder.

Thus, the number 43 is not divisible by 4.

Therefore, the correct answer is No.

To determine if 42 is divisible by 2, we apply the divisibility rule for 2:

• According to the divisibility rule, a number is divisible by 2 if its last digit is one of the even digits: 0, 2, 4, 6, or 8.

Let's check the last digit of 42:

• The last digit of 42 is 2.

• The digit 2 is an even number.

Since 2 is even, it follows that 42 is divisible by 2.

Therefore, the answer to the problem is Yes, which corresponds to choice 1.

To determine whether the number 30 is divisible by 10, we will apply the divisibility rule for 10.

According to this rule, a number is divisible by 10 if its last digit is 0. Let's check the number 30:

• Step 1: Examine the last digit of 30.
  The last digit of 30 is 0.
• Step 2: Apply the divisibility rule:
  Since the last digit is 0, 30 is divisible by 10.

Therefore, the conclusion is that 30 is divisible by 10. The correct answer is Yes, which corresponds to choice 1 in the provided options.

To solve this problem, we'll follow these steps:

• Step 1: Identify if 8 is an even number.
• Step 2: Apply the divisibility rule for 2.
• Step 3: Determine if there is any remainder when dividing 8 by 2.

Now, let's work through each step:
Step 1: Observe that the number 8 is an even number because it ends in 8. Even numbers are defined as those ending in 0, 2, 4, 6, or 8.
Step 2: According to the divisibility rule for 2, any even number is divisible by 2. Thus, 8 is divisible by 2.
Step 3: To further verify, perform the division: $8 \div 2 = 4$ with a remainder of 0, confirming that 8 is indeed divisible by 2.

Therefore, the solution to the problem is Yes, and the correct answer is the choice having "Yes".

To determine if 21 is divisible by 4, we apply the divisibility rule for 4.

The rule states that a number is divisible by 4 if the number formed by its last two digits is divisible by 4. Since 21 only has two digits, we consider the entire number.

Checking if 21 is divisible by 4:
We calculate $21 \div 4$.

The quotient is 5 with a remainder of 1, since $4 \times 5 = 20$ and $21 - 20 = 1$.

Since there is a remainder, 21 is not divisible by 4. According to the divisibility rule, if there is any remainder other than zero, the number is not divisible.

Therefore, the correct conclusion is that 21 is not divisible by 4, and thus the number 21 is not divisible by 4.

To determine if 61 is divisible by 10, we use the divisibility rule for 10:

• A number is divisible by 10 if and only if its last digit is 0.

Let's apply this rule to the number 61:

• The last digit of 61 is 1.
• Since 1 is not 0, 61 does not satisfy the divisibility rule for 10.

Therefore, we conclude that 61 is not divisible by 10.

Hence, the correct answer is: No.

To determine if 16 is divisible by 2, we simply apply the divisibility rule for 2. According to this rule, a number is divisible by 2 if its last digit is an even number, meaning the last digit must be 0, 2, 4, 6, or 8.

• Step 1: Identify the last digit of the number 16. The last digit of 16 is 6.
• Step 2: Check if the last digit 6 is even. Since 6 is an even number, this means 16 satisfies the divisibility rule for 2.

Therefore, the number 16 is indeed divisible by 2.

The correct choice, according to this analysis, is:

Yes

We will solve the problem of determining whether 16 is divisible by 4 using a straightforward division method:

Step 1: Perform the division of 16 by 4.
Dividing $16 \div 4 = 4$. This division results in an integer without a remainder.

Step 2: Check the result:
Since the quotient 4 is an integer and there is no remainder, 16 is divisible by 4.

In conclusion, since the division of 16 by 4 yields an integer, 16 is divisible by 4 without a remainder. Therefore, the number 16 is indeed divisible by 4.

Thus, the answer to the problem is Yes, corresponding to choice 1.

To determine if the number 60 is divisible by 4, we will apply the divisibility rule for 4:

• According to the rule, a number is divisible by 4 if the number formed by its last two digits is divisible by 4.
• In this case, the last two digits of 60 are "60".
• We need to check if 60 is divisible by 4. This involves dividing 60 by 4:

$\frac{60}{4} = 15$

The division yields a quotient of 15 with no remainder, which indicates that 60 is indeed divisible by 4.

Given that the quotient is a whole number, we can confidently conclude that the number 60 is divisible by 4.

Hence, the answer to the question is Yes.

To determine if the number 60 is divisible by 10, we will apply the divisibility rule for 10:

• Step 1: Identify the last digit of the number 60. The last digit is 0.
• Step 2: Apply the divisibility rule: A number is divisible by 10 if its last digit is 0.

Since the last digit of 60 is 0, we conclude that 60 is divisible by 10.

Therefore, the answer to the question is Yes.

To determine if the number 15 is divisible by 2, we will apply the rule for divisibility by 2:

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

Now, let's follow these steps:

Step 1: Identify the last digit of the number 15. The last digit is 5.

Step 2: Compare this digit with the criteria for divisibility by 2. The digit 5 is not in the set of digits {0, 2, 4, 6, 8}.

Since the last digit of 15 is not one of the digits that makes a number divisible by 2, 15 is not divisible by 2.

Therefore, the conclusion is clear: the number 15 is not divisible by 2.

To determine if the number 10 is divisible by 4, follow these steps:

• Step 1: Perform Division
  Divide 10 by 4. Calculate $\frac{10}{4}$.
• Step 2: Check Result for Integer
  If $\frac{10}{4} = 2.5$, the result is not an integer.
• Step 3: Confirm Remainder
  Determine the remainder when 10 is divided by 4. $10 \div 4$ gives a quotient of 2 and a remainder of 2.
• Step 4: Conclusion on Divisibility
  Since there is a remainder, 10 is not divisible by 4.

Therefore, the number 10 is not divisible by 4. The correct answer is No.

The answer is yes - every number that is divisible by 10 is divisible by 2.

This can be learned through the divisibility rules of each number.

We know that to identify a number divisible by 10, we need to examine its ones digit,

only numbers whose ones digit is 0 are divisible by 10,

for example: 30, 510, 15610

We know that numbers whose ones digit is 0 are actually even numbers,

and even numbers are divisible by 2 without a remainder.

Therefore, we can be certain - every number that is divisible by 10 is also divisible by 2.

It's important to understand that this is not necessarily true in reverse, not every number that is divisible by 2 is also divisible by 10!

To determine whether a number divisible by 2 is also divisible by 10, we need to analyze each condition separately:

• Divisibility by 2:
• A number is divisible by 2 if its last digit is an even number, namely 0, 2, 4, 6, or 8. For example, 12 and 34 are both divisible by 2 because their last digits are 2 and 4, respectively.
• Divisibility by 10:
• A number is divisible by 10 if its last digit is 0. For example, 20 and 150 are divisible by 10 because their last digits are 0.

Now, let us examine whether every number that meets the criteria for being divisible by 2 also meets the criteria for being divisible by 10:

• According to the rules, a number divisible by 2 ends with an even digit (0, 2, 4, 6, or 8). However, only those that end in 0 satisfy the condition for divisibility by 10.
• This means not every number divisible by 2 will end with a 0. For instance, the number 14 is divisible by 2, but ends with a 4, not 0. Therefore, it is not divisible by 10.

Thus, we conclude that a number divisible by 2 does not necessarily have its last digit as 0, so it is not always divisible by 10.

Therefore, the correct answer to the problem is No.

To determine if a number divisible by 4 must also be divisible by 10, we will apply the divisibility rules for both numbers.

The rule for divisibility by 4 is that the last two digits of the number form a number that is divisible by 4. For example, the number 8, or 112, or 236 is divisible by 4.

The rule for divisibility by 10 is that the number ends in 0. For example, the numbers 10, 30, 250, or 400 are divisible by 10.

Let's consider an example to illustrate the point. The number 8 is divisible by 4 because when divided by 4, it yields 2, which is an integer. However, 8 is not divisible by 10, as dividing 8 by 10 does not produce an integer. Therefore, a number that is divisible by 4 does not have to end in 0, which is required for divisibility by 10.

By analyzing these examples, we conclude that a number divisible by 4 is not necessarily divisible by 10. Specifically, divisibility by 4 depends on the last two digits, whereas divisibility by 10 depends on the last digit.

Therefore, the solution to the problem is that a number divisible by 4 will not necessarily be divisible by 10, making the answer No.