What are the factors of 360?
Understand the Problem
The question is asking for the factors of the number 360. To find the factors, we will identify all the numbers that divide 360 evenly.
Answer
The factors of 360 are $1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 60, 72, 90, 120, 180, 360$.
Answer for screen readers
The factors of 360 are: $1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 60, 72, 90, 120, 180, 360$.
Steps to Solve
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Start with the number 360 Identify the number whose factors you want to find. In this case, the number is 360.
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List all possible divisors Check all integers from 1 up to 360 to see which numbers divide 360 without leaving a remainder. You can do this by performing the division and checking if the result is a whole number.
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Identify even divisors For each possible divisor ( n ), perform the check: $$ \text{If } 360 \div n \text{ is an integer, then } n \text{ is a factor of } 360. $$
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Compile the list of factors After checking all integer divisors, compile a complete list of all numbers that divide 360 evenly.
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Final check Verify that you have included all divisors, and ensure none are duplicated.
The factors of 360 are: $1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 60, 72, 90, 120, 180, 360$.
More Information
360 is a highly composite number, meaning it has more factors than any smaller positive integer. Its factors are important in number theory and are useful in simplifying fractions or finding least common multiples.
Tips
- Failing to check each number systematically. It’s easy to skip numbers or repeat them. Make sure to check every integer up to 360.
- Forgetting to include 360 itself and 1 as factors. Always include the number and 1 when finding factors.
