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 105 and understand their properties.
The factors of 105 are: 1, 3, 5, 7, 15, 21, 35, and 105.
To find the factors of 105, we can follow these steps:
Determine the criteria for judging whether a number is a factor. A number is a factor of 105 if it divides 105 without leaving a remainder.
List all the numbers starting from 1 up to the given number, which is 105 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 105 by the number. If the division results in an integer value, then the number is a factor of 105.
Finally, collect all the numbers that are factors of 105.
Let's now provide a concise step-by-step solution using math expressions.
Determine the criteria: A number is a factor of 105 if it divides 105 without leaving a remainder.
List all the numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ..., 105.
Use each number as a divisor and verify whether it is a factor:
Collect all the factors: 1, 3, 5, 7, 15, 21, 35, and 105.
The pair factors of 105 are the factors that can be multiplied together to give the original number. In this case, the pair factors of 105 are: (1, 105), (3, 35), (5, 21), and (7, 15).
Negative pair factors are the pair factors where one factor is negative and the other is positive. For the factors of 105, 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 105, we can follow these steps:
Divide 105 by the smallest prime number, which is 2. Since 105 is not divisible by 2, we move to the next prime number.
Divide 105 by the next prime number, which is 3. 105 ÷ 3 = 35.
Divide 35 by the next prime number, which is 5. 35 ÷ 5 = 7.
The prime factorisation of 105 is 3 × 5 × 7.
Example: Find the factors of 105.
Solution: The factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105.
Explanation: We have already determined the factors of 105 in the previous sections.
Example: Determine the pair factors of 105.
Solution: The pair factors of 105 are (1, 105), (3, 35), (5, 21), and (7, 15).
Explanation: We can multiply each pair of factors to obtain the original number, which is 105.
Example: Find the prime factorisation of 105.
Solution: The prime factorisation of 105 is 3 × 5 × 7.
Explanation: We divided 105 by the smallest prime numbers until we obtained prime factors.
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 105 can be written as 1 × 3 × 5 × 7 or 1 · 3 · 5 · 7.
There are different types of factors, including:
Prime factors: Prime numbers that divide a given number without leaving a remainder.
Composite factors: Numbers that are not prime and divide a given number without leaving a remainder.
Pair factors: Factors that can be multiplied together to give the original number.
Negative factors: Factors that are negative numbers.
Question: Factors of 105?
Answer: The factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105.
In conclusion, the factors of 105 are the numbers that divide 105 without leaving a remainder. We can find these factors by listing all the numbers up to 105 and verifying their divisibility. The pair factors of 105 are (1, 105), (3, 35), (5, 21), and (7, 15). The prime factorisation of 105 is 3 × 5 × 7. Factors play a significant role in various mathematical concepts and are represented using symbols like × or ·.