Factors are numbers that can be multiplied together to get a given number. In this blog, we will explore the factors of 150 and understand their properties.
The factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
To find the factors of 150, we can follow these steps:
Determine the criteria for judging whether a number is a factor. A number is a factor of 150 if it divides 150 without leaving a remainder.
List all the numbers starting from 1 up to the given number, which is 150 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 150 by that number. If the division is exact, then the number is a factor.
Finally, collect all the numbers that are factors of 150.
Let's now go through a step-by-step solution to find the factors of 150.
The criteria for judging whether a number is a factor of 150 is that it should divide 150 without leaving a remainder.
List all the numbers starting from 1 up to 150: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ..., 150.
Use each number as a divisor and verify whether it is a factor by dividing 150 by that number. For example, when we divide 150 by 2, we get 75, which is an exact division. So, 2 is a factor of 150. Similarly, we can divide 150 by other numbers and check for exact divisions.
Collect all the numbers that are factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
The pair factors of 150 are the pairs of numbers that multiply together to give 150. For example, the pair factors of 150 are (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), and (10, 15).
The negative pair factors of 150 are the pairs of numbers, where one number is positive and the other is negative, that multiply together to give 150. For example, the negative pair factors of 150 are (-1, -150), (-2, -75), (-3, -50), (-5, -30), (-6, -25), and (-10, -15).
Prime factorisation is the process of expressing a number as a product of its prime factors. The prime factors of 150 are the prime numbers that divide 150 exactly.
The prime factorisation of 150 is 2 * 3 * 5^2, where 2, 3, and 5 are the prime factors.
Example: Find the factors of 150.
Solution: The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
Example: Find the pair factors of 150.
Solution: The pair factors of 150 are (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), and (10, 15).
Example: Find the prime factorisation of 150.
Solution: The prime factorisation of 150 is 2 * 3 * 5^2.
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 by writing the numbers next to each other. For example, the factors of 150 can be represented as 1 * 2 * 3 * 5 * 5 or simply as 1 2 3 5 5.
There are different types of factors based on their properties:
Prime Factors: Prime factors are the factors that are prime numbers.
Composite Factors: Composite factors are the factors that are composite numbers.
Pair Factors: Pair factors are the pairs of numbers that multiply together to give a given number.
Negative Pair Factors: Negative pair factors are the pairs of numbers, where one number is positive and the other is negative, that multiply together to give a given number.
Question: What are the factors of 150?
Answer: The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
Question: What is the prime factorisation of 150?
Answer: The prime factorisation of 150 is 2 * 3 * 5^2.
Question: What are the pair factors of 150?
Answer: The pair factors of 150 are (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), and (10, 15).
In conclusion, the factors of 150 are the numbers that divide 150 without leaving a remainder. We can find these factors by listing all the numbers up to 150 and checking for exact divisions. The pair factors and negative pair factors are the pairs of numbers that multiply together to give 150. The prime factorisation of 150 is 2 * 3 * 5^2. Factors play a significant role in various mathematical concepts and are represented using symbols like the multiplication symbol (*) or by writing the numbers next to each other.