Factors of a number refer to the numbers that divide the given number without leaving a remainder. In other words, factors are the numbers that can be multiplied together to obtain the original number. In this blog, we will explore the factors of 144 and discuss various related concepts.
The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
To find the factors of 144, we can follow these steps:
Determine the criteria for judging whether a number is a factor. A number is a factor of 144 if it divides 144 without leaving a remainder.
List all the numbers starting from 1 up to the given number, which is 144 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 144 by that number. If the division results in an integer value, then the number is a factor.
Finally, collect all the numbers that are factors of 144.
Let's now provide a concise step-by-step solution using math expressions.
Determine the criteria: A number, say 'x', is a factor of 144 if 144 divided by 'x' results in an integer value.
List all the numbers: Starting from 1 up to 144, we have the following numbers: 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, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, and 144.
Verify each number: Using math expressions, we divide 144 by each number and check if the division results in an integer value. If it does, then the number is a factor of 144. After performing these calculations, we find that the factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
The pair factors of 144 are the pairs of numbers that multiply together to give 144. For example, (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), and (9, 16) are the pair factors of 144.
The negative pair factors of 144 are the pairs of numbers, one positive and one negative, that multiply together to give 144. For example, (-1, -144), (-2, -72), (-3, -48), (-4, -36), (-6, -24), (-8, -18), and (-9, -16) are the negative pair factors of 144.
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 144 is: 2^4 * 3^2. This means that 144 can be expressed as the product of 2 raised to the power of 4 and 3 raised to the power of 2.
Example: Find the factors of 144.
Solution: The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
Example: Determine the pair factors of 144.
Solution: The pair factors of 144 are: (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), and (9, 16).
Example: Calculate the prime factorisation of 144.
Solution: The prime factorisation of 144 is: 2^4 * 3^2.
In mathematics, factors play a crucial role in various areas such as number theory, algebra, and arithmetic. They help us understand the properties and relationships between numbers. Factors are used in prime factorisation, finding common factors, simplifying fractions, solving equations, and many other mathematical operations.
In mathematics, factors are often represented using the multiplication symbol '×' or a dot '.'. For example, the factors of 144 can be written as 1 × 144, 2 × 72, 3 × 48, and so on.
There are different types of factors based on their properties and relationships with the given number. Some common types of factors include:
Prime Factors: Prime factors are the prime numbers that divide the 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.
Proper Factors: Proper factors are the factors of a number excluding the number itself.
Question: What are the factors of 144?
Answer: The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
Question: What is the prime factorisation of 144?
Answer: The prime factorisation of 144 is: 2^4 * 3^2.
Question: What are pair factors?
Answer: Pair factors are the pairs of numbers that multiply together to give a given number.
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.
Question: What are proper factors?
Answer: Proper factors are the factors of a number excluding the number itself.
In conclusion, factors of a number are the numbers that divide the given number without leaving a remainder. The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. Pair factors, negative pair factors, and prime factorisation are also discussed in detail. Factors are essential in various mathematical operations and have different types based on their properties.