What are the factors of 168?
Understand the Problem
The question is asking for the factors of the number 168, which involves identifying all numbers that can divide 168 without leaving a remainder.
Answer
The factors of 168 are: $1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168$.
Answer for screen readers
The factors of 168 are: $1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168$.
Steps to Solve
- Identify the definition of factors
Factors are numbers that divide another number completely, leaving no remainder.
- Start with the number 1
Since 1 is a factor of every integer, we include 1. We will then test each integer from 1 up to 168.
- Perform division to find factors
We will check each number to see if it divides 168 evenly. This can be done using a division operation: if ( 168 \div n ) has no remainder, then ( n ) is a factor. For example, we check:
$$ 168 \div 2 = 84 $$
Since there is no remainder, 2 is a factor.
- Continue checking up to the square root of 168
We will continue this process for integers up to ( \sqrt{168} ) because factors come in pairs. The square root of 168 is approximately 12.96, so we check integers from 1 to 12.
- List all factors found
After checking each integer, we will collect all the factors of 168 that we found.
- Write down the complete list of factors
The final step is to compile all identified factors into a single list.
The factors of 168 are: $1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168$.
More Information
All factors of a number can be found by testing divisibility. This can be useful in various mathematical applications, including simplifying fractions, finding the greatest common divisor, and solving problems related to multiples.
Tips
- Forgetting to check all numbers up to the square root of the target number; this can lead to missing factors.
- Not including 1 and the number itself, which are always factors for any integer.
