Understanding the factors of numbers is essential in mathematics. This guide will delve into the factors of 90, exploring different methods to find them and addressing common questions. Let's dive in!
Numbers are a fundamental part of our daily lives. Knowing how to work with them, especially understanding their factors, is crucial for solving various mathematical problems. Factors are the numbers that divide a given integer exactly without leaving a remainder.
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The factors of 90 are the numbers that divide 90 completely. These factors can be found by dividing 90 by numbers less than or equal to 90. The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Factors can also come in pairs. These pairs multiply together to give the original number, in this case, 90.
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| Pair Factors | Product |
|---|---|
| (1, 90) | 1 × 90 = 90 |
| (2, 45) | 2 × 45 = 90 |
| (3, 30) | 3 × 30 = 90 |
| (5, 18) | 5 × 18 = 90 |
| (6, 15) | 6 × 15 = 90 |
| (9, 10) | 9 × 10 = 90 |
| Pair Factors | Product |
|---|---|
| (-1, -90) | -1 × -90 = 90 |
| (-2, -45) | -2 × -45 = 90 |
| (-3, -30) | -3 × -30 = 90 |
| (-5, -18) | -5 × -18 = 90 |
| (-6, -15) | -6 × -15 = 90 |
| (-9, -10) | -9 × -10 = 90 |
There are several ways to find the factors of 90. Here are three common methods:
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Prime factorization involves breaking down 90 into its prime factors. The prime factorization of 90 is:
90=2×3×3×5
So, the prime factors of 90 are 2, 3, and 5. The complete list of factors is derived from these prime factors.
The listing method involves listing all numbers from 1 to 90 and checking which ones divide 90 evenly:
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
This is one of the simplest methods. You divide 90 by all integers less than or equal to 90. If the division results in a whole number, that divisor is a factor.
For example:
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Example 1: Find the positive factors of 90.
Answer: The positive factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Example 2: Find the negative factors of 90.
Answer: The negative factors of 90 are -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45, and -90.
Example 3: Find the prime factorization of 36.
Answer: The prime factorization of 36 is 2×2×3×3
The factor tree of 90 includes the pairs (1, 90), (2, 45), (3, 30), (5, 18), (6, 15), and (9, 10).
The first 10 multiples of 90 are: 90, 180, 270, 360, 450, 540, 630, 720, 810, and 900.
Yes, 90 is a factor of 360. The factors of 360 include: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
No, 90 is not a factor of 45. However, both numbers share common factors. The factors of 45 are 1, 3, 5, 9, 15, and 45, while the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.