Question

write all the factor pairs for 36. is 36 prime or composite? explain.

Explanation:

Step1: Find factor pairs of 36

A factor pair of a number is a set of two factors, which when multiplied together, give that number. We start with 1:

• \(1\times36 = 36\), so (1, 36) is a factor pair.
• \(2\times18 = 36\), so (2, 18) is a factor pair.
• \(3\times12 = 36\), so (3, 12) is a factor pair.
• \(4\times9 = 36\), so (4, 9) is a factor pair.
• \(6\times6 = 36\), so (6, 6) is a factor pair.

We stop here because if we go beyond 6, we will start repeating the factor pairs (e.g., \(9\times4\) is the same as \(4\times9\)).

Step2: Determine if 36 is prime or composite

A prime number has exactly two distinct positive divisors: 1 and itself. A composite number has more than two distinct positive divisors.
From the factor pairs above, the distinct positive divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Since there are more than two distinct positive divisors, 36 is composite.

Answer:

The factor pairs of 36 are (1, 36), (2, 18), (3, 12), (4, 9), (6, 6). 36 is composite because it has more than two distinct positive divisors (1, 2, 3, 4, 6, 9, 12, 18, 36).