Divisibility Rules for 2, 4 and 10: Identifying and defining elements

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.

We begin by reviewing the divisibility rules:

• A number is divisible by 10 if and only if its last digit is 0. This implies that the number can be expressed as $10k$, where $k$ is an integer.
• A number is divisible by 4 if the number formed by its last two digits is divisible by 4. For example, 112 is divisible by 4 because 12 (its last two digits) is divisible by 4.

Let's analyze these conditions:

Since any number that is divisible by 10 ends with a 0, examples would include 10, 20, 30, etc. Look at the last two digits of these numbers:

• For 10, the last two digits are 10, which is not divisible by 4 (since $\frac{10}{4} = 2.5$).
• For 20, the last two digits are 20, which is divisible by 4 (since $\frac{20}{4} = 5$).
• For 30, the last two digits are 30, which is not divisible by 4 (since $\frac{30}{4} = 7.5$).

From this analysis, it's clear that numbers like 10 and 30 are divisible by 10 but not by 4. Thus, it's possible for a number to be divisible by 10 without being divisible by 4.

Therefore, the answer to the question "If a number is divisible by 10, will it therefore be divisible by 4?" is no.

To solve this problem, we need to assess each provided choice against division rules for numbers ending in 0:

• Choice 1: "If the ones digit is 0, the number is divisible by 4."
  This statement is incorrect because having a ones digit of 0 doesn't ensure that the last two digits form a number divisible by 4. For example, 10 ends in 0 but isn’t divisible by 4.
• Choice 2: "If the ones digit is 0, the number is divisible by 2."
  This statement is correct, as any number ending in 0 is even, thus divisible by 2.
• Choice 3: "If the ones digit is 0, the number is divisible by 10."
  This statement is correct, as having a last digit of 0 ensures the number is divisible by 10.
• Choice 4: "Answers b and c are correct."
  Since both choice 2 (b) and choice 3 (c) are correct, this statement is also true.

Based on the analysis of each selection, the correct answer is: "Answers b and c are correct."

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."

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'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.".