Factors of 45 Using Prime Factorization
Introduction
Integers that can divide a number event are called its factors. The number in consideration here is 45 and the integers that divide it evenly are known as the factors of 45. There are a total of six factors of the number 45: 1, 3, 5, 9, 15 and 45. The numbers that are multiplied in pairs to produce 45 are the factor pairs of 45. These factor pairs can be either positive or negative. The factor pair of 45, for example, can be (1,45) or (-1, -45). We will learn about the factors of 45 in this article, as well as the positive and negative factor pairs of 45. We will also learn about the prime factorization of 45 and solve some examples.
Using Divisibility rules and Division to find the Factors of 45
Therefore, the factors of 45 are 1, 3, 5, 9, 15 and 45. And the factor pairs for 45 are (1, 45), (3, 15), and (5, 9).
Prime Factors of a number 45
Below, the factor tree is useful for learning about the prime factorization of 45. As 45 is a composite number.
Prime factorization of 45 is \(3^2\times 5\), this means 3 and 5 are the factors of 45. Also, we can say that 3 and 5 are the prime factors of 45.
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Positive Factor pairs of 45
The factor pairs of 45 are two factors when multiplied together, they produce the number 45. The following are some examples of the factor pairs of 45:
Rapid Recall
The factors of 45 are given below.
Solved Factors of 45 Examples
Example 1: Find the common factors of 45 and 24.
Solution:
The factors of 45 are 1, 3, 5, 9, 15, and 45.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Hence, the common factors of 45 and 24 are 1 and 3.
Example 2: Find the common factor of 45 and 15.
Solution:
The factors of 45 are 1, 3, 5, 9, 15, and 45.
The factors of 15 are 1, 3, 5, and 15.
Hence, the common factors of 45 and 15 are 1, 3, 5, and 15.
Example 3: John needs to decorate 45 bowls of mayonnaise and 36 bowls of ketchup for a dinner party. He wants to group them separately but such that there are equal number of bowls for both ketchup and mayonnaise. Find out the possible number of ways for him to do so.
Solution:
The common factors of 45 and 36 would give us the required ways to group the bowls.
The factors of 45 are 1, 3, 5, 9, 15, and 45.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
As the common factors of 45 and 36 are 1, 3, and 9 therefore John can group the bowls as follows:
- 1 bowl of mayonnaise and 1 bowl of ketchup
- 3 bowls of mayonnaise and 3 bowls of ketchup
- 9 bowls of mayonnaise and 9 bowls of ketchup.
Example 4: Find the common factors of 45 and 30.
Solution:
The factors of 45 are 1, 3, 5, 9, 15, and 45.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Hence, the common factors of 45 and 30 are 1, 3, 5, and 15.
Example 5: Find the common factors of 45 and 90.
Solution:
The factors of 45 are 1, 3, 5, 9, 15, and 45.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90
Hence, the common factors of 45 and 90 are 1, 3, 5, 9, 15, and 45.
1, 3, 5, 9, 15 and 45 are the factors of 45.
3 × 3 × 5 or \(3^2\) × 5 is the prime factorization of 45.
(1, 45), (3, 15)and (5, 9) are the positive pair factors of 45.
(-1, -45), (-3, -15) and (-5, -9) are the negative pair factors of 45.
Yes, 15 is a factor of 45. As 15 divides 45 exactly and leaves the remainder 0.