An integer divisor (also known as a factor) is an integer that divides another integer evenly, meaning it leaves no remainder.
Here's a more detailed explanation:
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Definition: An integer a is a divisor of an integer b if there exists another integer c such that b = a * c.
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Example: 7 is a divisor of 35 because 35 / 7 = 5, which is also an integer. This means 35 = 7 * 5.
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Alternative Terminology: When a is a divisor of b, we can also say:
- b is divisible by a.
- b is a multiple of a.
- a divides b. We often denote this as a | b.
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Non-Example: 3 is not a divisor of 10 because 10 / 3 = 3.333..., which is not an integer. There is a remainder.
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Examples:
- The divisors of 12 are: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12
- The divisors of 7 are: 1, -1, 7, -7 (7 is a prime number, so it's only divisible by 1 and itself).
- The divisors of 1 are: 1, -1
In summary, an integer divisor perfectly divides another integer without leaving any fractional remainder.
