Factors of a number refer to the numbers that divide the given number without leaving a remainder. In this blog, we will explore the factors of 180 and understand their properties.
The factors of 180 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
To find the factors of 180, follow these steps:
Determine the criteria for judging whether a number is a factor. A number is a factor of 180 if it divides 180 without leaving a remainder.
List all the numbers starting from 1 up to the given number, which is 180 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 180 by the number. If the division results in an integer value, then the number is a factor.
Finally, collect all the numbers that are factors of 180.
Let's now provide a concise step-by-step solution using math expressions.
Start with the number 1 and divide 180 by it: 180 ÷ 1 = 180. Since the division results in an integer value, 1 is a factor of 180.
Divide 180 by 2: 180 ÷ 2 = 90. Again, the division results in an integer value, so 2 is a factor of 180.
Continue this process for all numbers up to 180. The factors of 180 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
The pair factors of 180 are the factors that can be multiplied together to give the number 180. For example, the pair factors of 180 are (1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), and (10, 18).
Negative pair factors are the pair factors where one factor is negative and the other is positive. For example, (-1, -180), (-2, -90), (-3, -60), (-4, -45), (-5, -36), (-6, -30), (-9, -20), and (-10, -18) are the negative pair factors of 180.
Prime factorisation is the process of expressing a number as a product of its prime factors. To find the prime factorisation of 180, we divide it by prime numbers until we can no longer divide.
The prime factorisation of 180 is: 2 × 2 × 3 × 3 × 5 = 2^2 × 3^2 × 5.
Example: Find the factors of 180.
Solution: The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
Example: Find the pair factors of 180.
Solution: The pair factors of 180 are (1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), and (10, 18).
Example: Find the prime factorisation of 180.
Solution: The prime factorisation of 180 is 2^2 × 3^2 × 5.
In mathematics, factors are numbers that divide a given number without leaving a remainder. They play a crucial role in various mathematical concepts, such as prime factorisation, finding common factors, and solving equations.
In mathematics, factors are often represented using the multiplication symbol (×) or a dot (·). For example, the factors of 180 can be represented as 1 × 180, 2 × 90, 3 × 60, and so on.
There are different types of factors, including:
Prime Factors: Prime factors are the factors that are prime numbers. In the case of 180, the prime factors are 2, 3, and 5.
Pair Factors: Pair factors are the factors that can be multiplied together to give the original number. For example, (2, 90) is a pair factor of 180.
Negative Pair Factors: Negative pair factors are the pair factors where one factor is negative and the other is positive. For example, (-2, -90) is a negative pair factor of 180.
Question: What are the factors of 180?
Answer: The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
Question: What is the prime factorisation of 180?
Answer: The prime factorisation of 180 is 2^2 × 3^2 × 5.
Question: How do you find the pair factors of 180?
Answer: To find the pair factors of 180, you need to identify the numbers that can be multiplied together to give 180. For example, (2, 90) is a pair factor of 180.
Question: What are negative pair factors?
Answer: Negative pair factors are the pair factors where one factor is negative and the other is positive. For example, (-2, -90) is a negative pair factor of 180.
Question: What is the significance of factors in mathematics?
Answer: Factors are important in various mathematical concepts, such as prime factorisation, finding common factors, solving equations, and understanding the properties of numbers.