The remainder of an odd number when divided by 2 is always 1.
Here's a breakdown:
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Understanding Odd Numbers: Odd numbers are integers that cannot be evenly divided by 2. This means that when you divide an odd number by 2, you will always have a remainder.
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Mathematical Representation: Any odd number can be represented in the form of 2n + 1, where 'n' is any integer. When you divide (2n + 1) by 2, 2n is perfectly divisible leaving only the +1.
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Examples:
- 7 / 2 = 3 with a remainder of 1
- 15 / 2 = 7 with a remainder of 1
- 23 / 2 = 11 with a remainder of 1
- 101 / 2 = 50 with a remainder of 1
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Even Numbers vs. Odd Numbers: This is in contrast to even numbers, which are perfectly divisible by 2, leaving a remainder of 0.
In summary, the defining characteristic of an odd number is its inability to be divided evenly by 2, resulting in a remainder of 1.
