What are all the factors, the prime factorization, and factor pairs of 15?

Factors are the building blocks of numbers, essential to the study of mathematics. They are the numbers we multiply together to get another number. For instance, with the number 15, understanding its factors reveals its structure within the context of multiplication. Factors have a variety of applications, including simplifying fractions, finding least common multiples, and analyzing number patterns.

Factors of 15 are the whole numbers that divide 15 without leaving a remainder. To visually represent this, we can imagine a set of blocks that we’re dividing into equal smaller sets to demonstrate the multiplication process. The entire list of factors for the number 15 is 1, 3, 5, and 15.

• 1 x 15 = 15
• 3 x 5 = 15

To find the factors of 15, we employ the division method. This method involves dividing 15 by smaller integers and determining if the quotient is a whole number. If it is, that divisor is considered a factor of 15. Below is an example of how to apply this division method to discover the factors of 15:

• 15 ÷ 1 = 15, so 1 is a factor.
• 15 ÷ 3 = 5, so 3 is a factor.
• 15 ÷ 5 = 3, so 5 is a factor.
• 15 ÷ 15 = 1, so 15 is a factor.

When we attempt to divide 15 by any other integer, the result is not a whole number, for example, 15 ÷ 2 = 7.5.

Pair factors of 15 are two numbers that, when multiplied together, result in 15. These can be either positive or negative. Positive pair factors are:

• 1 x 15 = 15
• 3 x 5 = 15

And the negative pair factors are:

• -1 x -15 = 15
• -3 x -5 = 15

The prime factorization of a number breaks it down into its basic building blocks, which are prime numbers. For 15, the prime factorization is 3 x 5. We start by dividing 15 by its smallest prime factor, 3, which results in 5. As 5 is also a prime number, we stop there, and our factor tree diagram would show only two branches.

When it comes to the factors of 15, remember the following:

• The number 15 has a total of four factors: 1, 3, 5, and 15.
• The prime factors of 15 are 3 and 5.
• The pair factors (both positive and negative) demonstrate how two numbers can multiply to produce 15.
• The sum of the factors of 15 is 1 + 3 + 5 + 15 = 24.

• Exercise 1: What are the factors of 15?
• Exercise 2: Identify the pair factors of 15.
• Exercise 3: Determine the prime factorization of 15.

Solution 1: The factors of 15 are 1, 3, 5, and 15.

Solution 2: The positive pair factors of 15 are (1, 15) and (3, 5). The negative pair factors are (-1, -15) and (-3, -5).

Solution 3: The prime factorization of 15 is 3 x 5.