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 216 and understand their properties.
The factors of 216 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
To find the factors of 216, we can follow these steps:
Determine the criteria for judging whether a number is a factor. A number is a factor of 216 if it divides 216 without leaving a remainder.
List all the numbers starting from 1 up to the given number, which is 216 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 216 by the number. If the division results in an integer value, then the number is a factor of 216.
Finally, collect all the numbers that are factors of 216.
Let's now provide a concise step-by-step solution using math expressions.
Determine the criteria: A number, say 'x', is a factor of 216 if 216 divided by 'x' results in an integer value.
List all the numbers: Starting from 1 up to 216, we have the numbers 1, 2, 3, 4, 5, ..., 216.
Verify each number: Divide 216 by each number and check if the division results in an integer value.
Collect the factors: The numbers that divide 216 without leaving a remainder are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
The pair factors of 216 are the pairs of numbers that multiply together to give 216. For example, the pair factors of 216 are (1, 216), (2, 108), (3, 72), (4, 54), (6, 36), (8, 27), (9, 24), and (12, 18).
The negative pair factors of 216 are the pairs of numbers, one positive and one negative, that multiply together to give 216. For example, the negative pair factors of 216 are (-1, -216), (-2, -108), (-3, -72), (-4, -54), (-6, -36), (-8, -27), (-9, -24), and (-12, -18).
Prime factorisation of a number involves expressing the number as a product of its prime factors. The prime factors of 216 are the prime numbers that divide 216 without leaving a remainder.
The prime factorisation of 216 is 2^3 × 3^3, where '^' denotes exponentiation. This means that 216 can be expressed as the product of three 2's and three 3's.
Example: Find the factors of 216.
Solution: The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
Example: Determine the pair factors of 216.
Solution: The pair factors of 216 are (1, 216), (2, 108), (3, 72), (4, 54), (6, 36), (8, 27), (9, 24), and (12, 18).
Example: What is the prime factorisation of 216?
Solution: The prime factorisation of 216 is 2^3 × 3^3.
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 '×'. For example, the factors of 216 can be written as 1 × 216, 2 × 108, 3 × 72, and so on.
There are different types of factors, including:
Prime Factors: Prime factors are the prime numbers that divide a given number without leaving a remainder.
Pair Factors: Pair factors are the pairs of numbers that multiply together to give the given number.
Negative Pair Factors: Negative pair factors are the pairs of numbers, one positive and one negative, that multiply together to give the given number.
Question: What are the factors of 216?
Answer: The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
Question: What is the prime factorisation of 216?
Answer: The prime factorisation of 216 is 2^3 × 3^3.
Question: How do you find the factors of 216?
Answer: To find the factors of 216, list all the numbers from 1 to 216 and divide 216 by each number. If the division results in an integer value, then the number is a factor of 216.
Question: What are pair factors?
Answer: Pair factors are the pairs of numbers that multiply together to give a given number. For example, the pair factors of 216 are (1, 216), (2, 108), (3, 72), and so on.
Question: What are negative pair factors?
Answer: Negative pair factors are the pairs of numbers, one positive and one negative, that multiply together to give a given number. For example, the negative pair factors of 216 are (-1, -216), (-2, -108), (-3, -72), and so on.
In conclusion, the factors of 216 are the numbers that divide 216 without leaving a remainder. They play a significant role in various mathematical concepts and calculations.