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 225 and understand their properties.
The factors of 225 are: 1, 3, 5, 9, 15, 25, 45, 75, and 225.
To find the factors of 225, we can follow these steps:
Determine the criteria for judging whether a number is a factor. A number is a factor of 225 if it divides 225 without leaving a remainder.
List all the numbers starting from 1 up to the given number, which is 225 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 225 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 225.
Let's now go through a step-by-step solution to find the factors of 225.
The criteria for judging whether a number is a factor of 225 is that it should divide 225 without leaving a remainder.
List all the numbers starting from 1 up to 225:
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, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, and 225.
Use each number as a divisor and verify whether it is a factor of 225:
Finally, we collect all the numbers that are factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, and 225.
Pair factors are the pairs of numbers that multiply together to give the original number. For the factors of 225, the pair factors are:
Negative pair factors are the pairs of numbers where one number is positive and the other is negative, and their product is equal to the original number. For the factors of 225, there are no negative pair factors since all the factors are positive.
Prime factorisation is the process of expressing a number as a product of its prime factors. To find the prime factorisation of 225, we can start by dividing it by the smallest prime number, which is 2. However, 225 is not divisible by 2. Next, we divide it by the next prime number, which is 3. 225 divided by 3 gives us 75. Again, 75 is divisible by 3, resulting in 25. Finally, 25 is divisible by 5, giving us 5. Therefore, the prime factorisation of 225 is 3 × 3 × 5 × 5, which can be written as 3² × 5².
Example: Find the factors of 225.
Solution: The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.
Example: Determine the pair factors of 225.
Solution: The pair factors of 225 are (1, 225), (3, 75), (5, 45), (9, 25), and (15, 15).
Example: What is the prime factorisation of 225?
Solution: The prime factorisation of 225 is 3² × 5².
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. Factors help us understand the properties and relationships between numbers.
In mathematics, factors are often represented using the multiplication symbol (×) or a dot (·). For example, we can write the factors of 225 as 1 × 225, 3 × 75, 5 × 45, 9 × 25, 15 × 15, or as pairs (1, 225), (3, 75), (5, 45), (9, 25), and (15, 15).
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 factors that are prime numbers. They cannot be further divided into smaller factors.
Composite Factors: Composite factors are the factors that are composite numbers. They can be further divided into smaller factors.
Pair Factors: Pair factors are the pairs of numbers that multiply together to give the original number.
Negative Pair Factors: Negative pair factors are the pairs of numbers where one number is positive and the other is negative, and their product is equal to the original number.
Proper Factors: Proper factors are the factors of a number excluding the number itself.
Question: What are the factors of 225?
Answer: The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.
Question: What is the prime factorisation of 225?
Answer: The prime factorisation of 225 is 3² × 5².
Question: Are there any negative pair factors of 225?
Answer: No, there are no negative pair factors of 225 since all the factors are positive.
Question: How can factors be used in solving equations?
Answer: Factors can be used to simplify equations by factoring out common terms or finding roots of equations. They help in solving polynomial equations and finding solutions to algebraic problems.
Question: Can factors be decimals or fractions?
Answer: Factors are typically whole numbers, but in some cases, they can be decimals or fractions. However, the concept of factors is primarily used for whole numbers.