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 75 and understand their properties.
The factors of 75 are: 1, 3, 5, 15, 25, and 75.
To find the factors of 75, we can follow these steps:
Determine the criteria for judging whether a number is a factor. A number is a factor of 75 if it divides 75 without leaving a remainder.
List all the numbers starting from 1 up to the given number, which is 75 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 75 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 75.
Let's now go through a step-by-step solution to find the factors of 75.
We start by listing all the numbers from 1 to 75: 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.
Now, we divide 75 by each number and check if the division results in an integer value.
Collecting all the numbers that resulted in an integer value, we get the factors of 75: 1, 3, 5, 15, 25, and 75.
The pair factors of 75 are the factors that can be multiplied together to give the original number. In the case of 75, the pair factors are: (1, 75) and (3, 25).
Negative pair factors are the pair factors where one factor is negative and the other is positive. For 75, the negative pair factors are: (-1, -75) and (-3, -25).
Prime factorisation is the process of expressing a number as a product of its prime factors. To find the prime factorisation of 75, we divide it by prime numbers until we can no longer divide.
75 ÷ 3 = 25 25 ÷ 5 = 5
Therefore, the prime factorisation of 75 is 3 × 5.
Example: Find the factors of 75.
Solution: The factors of 75 are 1, 3, 5, 15, 25, and 75.
Example: Determine the pair factors of 75.
Solution: The pair factors of 75 are (1, 75) and (3, 25).
Example: What is the prime factorisation of 75?
Solution: The prime factorisation of 75 is 3 × 5.
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 a dot (·). For example, the factors of 75 can be written as 1 × 75 or 1 · 75.
There are different types of factors, including:
Prime Factors: Prime factors are the factors that are prime numbers. They cannot be further divided into smaller factors.
Composite Factors: Composite factors are the factors that are not prime numbers. They can be further divided into smaller factors.
Pair Factors: Pair factors are the factors that can be multiplied together to give the original number.
Negative Pair Factors: Negative pair factors are the pair factors where one factor is negative and the other is positive.
Q: What are the factors of 75?
A: The factors of 75 are 1, 3, 5, 15, 25, and 75.
Q: What is the prime factorisation of 75?
A: The prime factorisation of 75 is 3 × 5.
Q: How do you find the factors of a number?
A: To find the factors of a number, list all the numbers up to the given number and divide the number by each of these numbers. If the division results in an integer value, then the number is a factor.
Q: What is the significance of factors in mathematics?
A: Factors are important in various mathematical concepts, such as prime factorisation, finding common factors, and solving equations. They help in understanding the properties and relationships between numbers.
Q: Can negative numbers be factors of a positive number?
A: Yes, negative numbers can be factors of a positive number. The pair factors of a number can include both positive and negative numbers.
In conclusion, the factors of 75 are 1, 3, 5, 15, 25, and 75. These factors can be used in various mathematical operations and concepts. Understanding factors is essential for solving mathematical problems and exploring the properties of numbers.