What are the factors of 360?
Understand the Problem
The question is asking for the factors of the number 360. Factors are the integers that can be multiplied together to produce the original number. To solve this, we can identify all the integers that divide 360 without leaving a remainder.
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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Identify the starting point Begin with the number 360. We will test each integer starting from 1 to see if it divides evenly into 360.
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Check for divisibility To determine if a number $n$ is a factor of 360, we can check if $360 \mod n = 0$ (which means 360 divided by $n$ leaves no remainder).
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Test integers sequentially Start testing integers from 1 up to 360.
- For example, test 1: $360 \mod 1 = 0$, so 1 is a factor.
- Next, test 2: $360 \mod 2 = 0$, so 2 is a factor.
- Continue this process up to 360.
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List all factors Keep a list of all integers that divide 360 without a remainder. You'll find that some of these factors include 1, 2, 3, 4, 5, 6, etc.
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Complete the factor list Continue until you find all factors, compiling the full list. The last factor to find will be 360 itself.
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 has a rich factor structure, as it is a composite number. It is the product of prime factors: $360 = 2^3 \times 3^2 \times 5^1$. Understanding how these primes combine reveals its many factors.
Tips
- Skipping numbers while checking divisibility. Make sure to test every integer up to 360.
- Confusing factors with multiples. Remember, factors divide the number evenly, while multiples are produced by multiplying the number by integers.
