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 need to identify all the integers that can be multiplied together to produce 360.
Answer
The factors of 360 are: $1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360$.
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, 45, 60, 72, 90, 120, 180, 360.
Steps to Solve
- Identify the number to factor
We need to find the factors of the number 360.
- Start with the smallest integer
Begin with the smallest integer, which is 1, and divide 360 by it: $$ 360 \div 1 = 360 $$ So, both 1 and 360 are factors.
- Continue with increasing integers
Next, move to 2: $$ 360 \div 2 = 180 $$ So, 2 and 180 are factors.
- Check for divisibility with each integer
Continue checking divisibility for each integer up to the square root of 360 (which is approximately 19):
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For 3, $$ 360 \div 3 = 120 $$ Factors: 3 and 120.
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For 4, $$ 360 \div 4 = 90 $$ Factors: 4 and 90.
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For 5, $$ 360 \div 5 = 72 $$ Factors: 5 and 72.
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For 6, $$ 360 \div 6 = 60 $$ Factors: 6 and 60.
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For 8, $$ 360 \div 8 = 45 $$ Factors: 8 and 45.
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For 9, $$ 360 \div 9 = 40 $$ Factors: 9 and 40.
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For 10, $$ 360 \div 10 = 36 $$ Factors: 10 and 36.
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For 12, $$ 360 \div 12 = 30 $$ Factors: 12 and 30.
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For 15, $$ 360 \div 15 = 24 $$ Factors: 15 and 24.
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For 18, $$ 360 \div 18 = 20 $$ Factors: 18 and 20.
- Compile all the factors
Now list all the factors found: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.
The factors of 360 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.
More Information
The number 360 is a highly composite number, meaning it has more divisors than any smaller positive integer. It is also used in various contexts, such as in geometry (a circle has 360 degrees).
Tips
A common mistake is to overlook one of the factors when listing them, especially when dividing by larger numbers. Always ensure to check divisibility methodically, incrementing your divisor.
