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

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.

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 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 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.

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 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

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 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 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 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 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 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 solve this problem, we'll apply divisibility rules:

• Statement 1: "If the ones digit is 4, the number is divisible by 4." This is incorrect. A number is divisible by 4 if the last two digits form a number divisible by 4, not just based on the ones digit.
• Statement 2: "If the ones digit is 2, the number is divisible by 2." This is correct, as having an ones digit of 2 indicates the number is even, thus divisible by 2.
• Statement 3: "If the ones digit is 6, the number is divisible by 10." This is incorrect. A number is divisible by 10 only if its ones digit is 0.
• Statement 4: "All correct answers." This statement cannot be true because statements 1 and 3 are incorrect based on the divisibility rules.

Therefore, the correct statement based on the divisibility rules is choice 2: "If the ones digit is 2, the number is divisible by 2.".

To solve this problem, we'll examine the divisibility conditions:

• Step 1: Evaluate divisibility by 2
  A number is divisible by 2 if its ones digit is any even number: 0, 2, 4, 6, 8. Here, since 4 is an even number, any number ending in 4 is indeed divisible by 2.
• Step 2: Evaluate divisibility by 4
  A number is divisible by 4 if the last two digits form a number divisible by 4.
  For example, the number 24 ends in 4 but is indeed divisible by 4 (24 divided by 4 is an integer), however, if the number was 34, it is not divisible by 4.
  Therefore, the statement "if the ones digit is 4, the number is divisible by 4" is not universally correct.
• Step 3: Evaluate divisibility by 10
  A number is divisible by 10 only when its ones digit is 0. Since 4 is not 0, it does not satisfy this condition.

Based on these evaluations, we conclude that the correct statement is: If the ones digit is 4, the number is divisible by 2.

To solve this problem, we need to evaluate the divisibility of a number whose ones digit is 2, based on the relevant divisibility rules:

• Divisibility by 2: A number is divisible by 2 if its ones digit is an even number, specifically 0, 2, 4, 6, or 8. Since the number ends in 2, it satisfies this condition and is divisible by 2.
• Divisibility by 4: For a number to be divisible by 4, its last two digits should form a number divisible by 4. Since the problem specifies only the ones digit as 2, additional information about the preceding digits is necessary, making this rule inapplicable solely based on the ones digit.
• Divisibility by 10: A number is divisible by 10 if its ones digit is 0. The digit 2 does not satisfy this rule.
• Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3. Since we do not have information about divisibility by 3, this condition cannot be verified.

Therefore, from the list of choices, the statement about the ones digit being 2 that is true is: "If the ones digit is 2, the number is divisible by 2."