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 81 and understand their properties.
The factors of 81 are: 1, 3, 9, 27, and 81.
To find the factors of 81, we can follow these steps:
Determine the criteria for judging whether a number is a factor. A number is a factor of 81 if it divides 81 without leaving a remainder.
List all the numbers starting from 1 up to the given number, which is 81 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 81 by the number. If the division results in an integer value, then the number is a factor of 81.
Finally, collect all the numbers that satisfy the criteria and obtain the factors of 81.
Let's now provide a concise step-by-step solution using math expressions:
Determine the criteria: A number, x, is a factor of 81 if 81 % x = 0.
List all the numbers: 1, 2, 3, 4, 5, ..., 81.
Verify each number as a factor:
Collect the factors: 1, 3, 9, 27, and 81.
The pair factors of 81 are the pairs of numbers that multiply together to give 81. In this case, the pair factors of 81 are: (1, 81) and (3, 27).
Negative pair factors of 81 are the pairs of numbers, one positive and one negative, that multiply together to give 81. For example, (-1, -81) and (-3, -27) are negative pair factors of 81.
Prime factorisation of a number involves expressing the number as a product of its prime factors. To find the prime factorisation of 81, we can follow these steps:
Start with the smallest prime number, which is 2.
Divide 81 by 2. Since 81 is not divisible by 2, move to the next prime number, which is 3.
Divide 81 by 3. 81 divided by 3 gives 27.
Divide 27 by 3. 27 divided by 3 gives 9.
Divide 9 by 3. 9 divided by 3 gives 3.
Divide 3 by 3. 3 divided by 3 gives 1.
The prime factorisation of 81 is 3^4, where "^" represents exponentiation.
Example: Find the factors of 81. Solution: The factors of 81 are 1, 3, 9, 27, and 81.
Example: Determine the pair factors of 81. Solution: The pair factors of 81 are (1, 81) and (3, 27).
Example: What are the negative pair factors of 81? Solution: The negative pair factors of 81 are (-1, -81) and (-3, -27).
In mathematics, factors are numbers that divide another 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 symbol "∣" (vertical bar). For example, we can write "3 ∣ 9" to indicate that 3 is a factor of 9.
There are two types of factors: prime factors and composite factors.
Question: What are the factors of 81? Answer: The factors of 81 are 1, 3, 9, 27, and 81.
Question: How do I find the pair factors of 81? Answer: The pair factors of 81 are (1, 81) and (3, 27).
Question: What is the prime factorisation of 81? Answer: The prime factorisation of 81 is 3^4.
Question: What are the negative pair factors of 81? Answer: The negative pair factors of 81 are (-1, -81) and (-3, -27).
Question: How are factors used in solving equations? Answer: Factors are used to simplify equations by factoring out common terms or finding roots of equations. They help in solving polynomial equations and finding solutions.