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Determine whether a number is composite

A composite number is a whole number greater than 1 that has more than two positive factors, including 1 and itself; equivalently, it can be expressed as a product of two smaller whole numbers. Within numbers through 100, this understanding includes identifying factor pairs or rectangular arrays, distinguishing composite numbers from primes with exactly two factors, and recognizing that 1 is neither prime nor composite; it supports later work with factorization and divisibility.

Detailed Explanation: Determine whether a number is composite

A composite number is a whole number greater than 11 that has more than two positive factors. Another way to recognize one is to write it as a product of two smaller whole numbers.

Example: Is (18)(18) composite?

  1. Find factor pairs for (18)(18).
1×18=18 1\times18=18 2×9=18 2\times9=18 3×6=18 3\times6=18
  1. List the factors:
1, 2, 3, 6, 9, 18 1,\ 2,\ 3,\ 6,\ 9,\ 18
  1. Since (18)(18) has more than two factors, it is composite. It is also composite because it can be written as
18=2×9, 18=2\times9,

where both factors are smaller than (18)(18).

A number with exactly two factors, 11 and itself, is prime. The number 11 is neither prime nor composite.

Learn by doing: Determine whether a number is composite

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Is the Number Prime or Composite


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