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Chapter 2: Problem 245

In the following exercises, find all the factors of the given number. $$ 60 $$

Short Answer

Expert verified
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Step by step solution

01

- Understand the concept of factors

A factor of a number is an integer that can be divided evenly into that number without leaving a remainder.
02

- List the pairs of numbers that multiply to 60

Start by finding the pairs of numbers whose product is 60. Begin with 1 and 60: 1 脳 60 = 60
03

- Continue finding factor pairs

Next, try 2: 2 脳 30 = 60Next, try 3: 3 脳 20 = 60Continue with 4: 4 脳 15 = 60Try 5: 5 脳 12 = 60Finally, with 6: 6 脳 10 = 60
04

- Check for completeness

Verify that we have found all pairs by continuing until the pairs start to repeat or the multiplication becomes greater than 60.
05

- List all factors

Once all pairs are found, list all the unique numbers involved in the pairs: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

integers
Let's start by understanding what integers are. Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. For example, -3, 0, and 4 are all integers. When working with factors, we focus on positive integers because factors are positive numbers that divide another number without leaving a remainder.
multiplication pairs
Multiplication pairs are pairs of numbers that, when multiplied together, give a particular product. For instance, the pairs of numbers that multiply to 60 are called multiplication pairs of 60. Finding these pairs helps identify the factors of a number.

To find these pairs, you can start with 1 and the number itself:

  • 1 脳 60 = 60
  • 2 脳 30 = 60
  • 3 脳 20 = 60
  • 4 脳 15 = 60
  • 5 脳 12 = 60
  • 6 脳 10 = 60
Continue looking for pairs until the numbers in the pairs start to repeat or become greater than the number you are factoring. This ensures you have a complete list of multiplication pairs.

By understanding multiplication pairs, it becomes easier to identify all the factors of a number.
divisibility
Divisibility is the ability for one number to be divided by another without leaving a remainder. It's crucial for finding factors. To determine factor pairs, we test for divisibility by smaller integers.

Here's how you can check for divisibility:
  • A number is divisible by 2 if it's even.
  • A number is divisible by 3 if the sum of its digits is divisible by 3.
  • A number is divisible by 5 if it ends in 0 or 5.
Using these simple divisibility rules helps you quickly identify factors of a number. For 60, checking for divisibility by 2, 3, and 5 helps us find pairs like 2 脳 30, 3 脳 20, and 5 脳 12.

Understanding divisibility rules makes finding factors more straightforward and ensures no factor is missed.

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Most popular questions from this chapter

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