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 108 and understand their properties.
The factors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
To find the factors of 108, we can follow these steps:
Determine the criteria for judging whether a number is a factor. A number is a factor of 108 if it divides 108 without leaving a remainder.
List all the numbers starting from 1 up to the given number, which is 108 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 108 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 108.
Let's now go through a step-by-step solution to find the factors of 108.
We start by listing all the numbers from 1 to 108:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108
Now, we divide 108 by each number and check if the division results in an integer value:
From the above calculations, we can see that the numbers 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108 are the factors of 108.
The pair factors of 108 are the pairs of numbers that multiply together to give 108. For example, the pair factors of 108 are (1, 108), (2, 54), (3, 36), (4, 27), (6, 18), and (9, 12).
The negative pair factors of 108 are the pairs of numbers, one positive and one negative, that multiply together to give 108. For example, the negative pair factors of 108 are (-1, -108), (-2, -54), (-3, -36), (-4, -27), (-6, -18), and (-9, -12).
Prime factorisation of a number involves expressing the number as a product of its prime factors. The prime factors are the prime numbers that divide the given number without leaving a remainder.
The prime factorisation of 108 is 2^2 × 3^3. This means that 108 can be expressed as the product of 2 raised to the power of 2 and 3 raised to the power of 3.
Example: Find the factors of 108.
Solution: The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Example: Determine the pair factors of 108.
Solution: The pair factors of 108 are (1, 108), (2, 54), (3, 36), (4, 27), (6, 18), and (9, 12).
Example: What is the prime factorisation of 108?
Solution: The prime factorisation of 108 is 2^2 × 3^3.
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 multiplication symbol (×) or a dot (·). For example, the factors of 108 can be represented as 1 × 108, 2 × 54, 3 × 36, and so on.
There are different types of factors based on their properties:
Prime Factors: Prime factors are the factors that are prime numbers. In the case of 108, the prime factors are 2 and 3.
Pair Factors: Pair factors are the pairs of numbers that multiply together to give the original number. For example, the pair factors of 108 are (1, 108), (2, 54), (3, 36), and so on.
Negative Pair Factors: Negative pair factors are the pairs of numbers, one positive and one negative, that multiply together to give the original number. For example, the negative pair factors of 108 are (-1, -108), (-2, -54), (-3, -36), and so on.
Question: What are the factors of 108? Answer: The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Question: What is the prime factorisation of 108? Answer: The prime factorisation of 108 is 2^2 × 3^3.
Question: What are pair factors? Answer: Pair factors are the pairs of numbers that multiply together to give a specific number. For example, the pair factors of 108 are (1, 108), (2, 54), (3, 36), 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 specific number. For example, the negative pair factors of 108 are (-1, -108), (-2, -54), (-3, -36), and so on.
Question: How are factors used in mathematics? Answer: Factors are used in various mathematical concepts, such as prime factorisation, finding common factors, solving equations, and determining divisibility. They help in understanding the properties and relationships between numbers.