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Answer :
- To check if a number 'a' is a multiple of a number 'b', divide 'a' by 'b'.
- If the result is an integer (remainder is zero), 'a' is a multiple of 'b'.
- 1842112 is not a multiple of 3036412, and 3036412 is not a multiple of 1842112.
- Neither 1842112 nor 3036412 are multiples of 36, as both leave a remainder of 28 when divided by 36.
### Explanation
1. Understanding the Problem
The problem asks us to understand how to check if one number is a multiple of another. We are given two numbers, 1842112 and 3036412, and an incomplete long division problem.
2. Checking Multiples
To check if a number 'a' is a multiple of another number 'b', we divide 'a' by 'b'. If the result is an integer (i.e., the remainder is zero), then 'a' is a multiple of 'b'. In other words, if $a = k
\times b$ for some integer 'k', then 'a' is a multiple of 'b'.
3. Checking 1842112 vs 3036412
Let's check if 1842112 is a multiple of 3036412. When we divide 1842112 by 3036412, we get approximately 0.6066, which is not an integer. Therefore, 1842112 is not a multiple of 3036412.
4. Checking 3036412 vs 1842112
Now, let's check if 3036412 is a multiple of 1842112. When we divide 3036412 by 1842112, we get approximately 1.6483, which is not an integer. Therefore, 3036412 is not a multiple of 1842112.
5. Analyzing the Long Division
The incomplete long division $36 \times 386 \overline{)24}$ is unclear and doesn't seem directly related to the problem of checking multiples. It might be an example of a division problem, but it's incomplete and doesn't offer any specific insight into the original question. However, we can check if 1842112 and 3036412 are multiples of 36.
6. Checking Multiples of 36 for 1842112
When we divide 1842112 by 36, we get approximately 51169.777. The integer part is 51169, and the remainder is 28, since $1842112 = 51169 \times 36 + 28$. Therefore, 1842112 is not a multiple of 36.
7. Checking Multiples of 36 for 3036412
When we divide 3036412 by 36, we get approximately 84344.777. The integer part is 84344, and the remainder is 28, since $3036412 = 84344 \times 36 + 28$. Therefore, 3036412 is not a multiple of 36.
8. Final Summary
In summary, to check if a number 'a' is a multiple of a number 'b', divide 'a' by 'b'. If the remainder is 0, then 'a' is a multiple of 'b'. Otherwise, it is not.
### Examples
Understanding multiples is crucial in everyday situations like dividing quantities equally. For instance, if you have 48 cookies and want to share them equally among friends, knowing that 48 is a multiple of 2, 3, 4, 6, 8, 12, 16, and 24 helps you quickly determine how many cookies each friend will receive if you have 2, 3, 4, etc., friends. This concept is also vital in scheduling, resource allocation, and many other practical scenarios where equal distribution or division is required.
- If the result is an integer (remainder is zero), 'a' is a multiple of 'b'.
- 1842112 is not a multiple of 3036412, and 3036412 is not a multiple of 1842112.
- Neither 1842112 nor 3036412 are multiples of 36, as both leave a remainder of 28 when divided by 36.
### Explanation
1. Understanding the Problem
The problem asks us to understand how to check if one number is a multiple of another. We are given two numbers, 1842112 and 3036412, and an incomplete long division problem.
2. Checking Multiples
To check if a number 'a' is a multiple of another number 'b', we divide 'a' by 'b'. If the result is an integer (i.e., the remainder is zero), then 'a' is a multiple of 'b'. In other words, if $a = k
\times b$ for some integer 'k', then 'a' is a multiple of 'b'.
3. Checking 1842112 vs 3036412
Let's check if 1842112 is a multiple of 3036412. When we divide 1842112 by 3036412, we get approximately 0.6066, which is not an integer. Therefore, 1842112 is not a multiple of 3036412.
4. Checking 3036412 vs 1842112
Now, let's check if 3036412 is a multiple of 1842112. When we divide 3036412 by 1842112, we get approximately 1.6483, which is not an integer. Therefore, 3036412 is not a multiple of 1842112.
5. Analyzing the Long Division
The incomplete long division $36 \times 386 \overline{)24}$ is unclear and doesn't seem directly related to the problem of checking multiples. It might be an example of a division problem, but it's incomplete and doesn't offer any specific insight into the original question. However, we can check if 1842112 and 3036412 are multiples of 36.
6. Checking Multiples of 36 for 1842112
When we divide 1842112 by 36, we get approximately 51169.777. The integer part is 51169, and the remainder is 28, since $1842112 = 51169 \times 36 + 28$. Therefore, 1842112 is not a multiple of 36.
7. Checking Multiples of 36 for 3036412
When we divide 3036412 by 36, we get approximately 84344.777. The integer part is 84344, and the remainder is 28, since $3036412 = 84344 \times 36 + 28$. Therefore, 3036412 is not a multiple of 36.
8. Final Summary
In summary, to check if a number 'a' is a multiple of a number 'b', divide 'a' by 'b'. If the remainder is 0, then 'a' is a multiple of 'b'. Otherwise, it is not.
### Examples
Understanding multiples is crucial in everyday situations like dividing quantities equally. For instance, if you have 48 cookies and want to share them equally among friends, knowing that 48 is a multiple of 2, 3, 4, 6, 8, 12, 16, and 24 helps you quickly determine how many cookies each friend will receive if you have 2, 3, 4, etc., friends. This concept is also vital in scheduling, resource allocation, and many other practical scenarios where equal distribution or division is required.
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