Factors are numbers that can be multiplied together to get a given number. In this blog, we will explore the factors of 98 and understand their properties.
The factors of 98 are: 1, 2, 7, 14, 49, and 98.
To find the factors of 98, we can follow these steps:
Determine the criteria for judging whether a number is a factor. A number is a factor of another number if it divides it evenly without leaving a remainder.
List all the numbers starting from 1 up to the given number, which is 98 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 98 by that number. If the division is exact, without any remainder, then the number is a factor.
Finally, collect all the numbers that are factors of 98.
Let's now go through a step-by-step solution to find the factors of 98.
The criteria for judging whether a number is a factor of 98 is that it should divide 98 evenly without leaving a remainder.
List all the numbers starting from 1 up to 98: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ..., 98.
Use each number as a divisor and verify whether it is a factor by dividing 98 by that number. For example, let's check if 2 is a factor of 98: 98 ÷ 2 = 49. Since the division is exact, without any remainder, 2 is a factor of 98. Similarly, we can check for other numbers.
Collect all the numbers that are factors of 98: 1, 2, 7, 14, 49, and 98.
The pair factors of 98 are the factors that can be multiplied together to get 98. In this case, the pair factors are: (1, 98) and (2, 49).
The negative pair factors of 98 are the pair factors where one factor is negative and the other is positive. In this case, the negative pair factors are: (-1, -98) and (-2, -49).
Prime factorisation is the process of expressing a number as a product of its prime factors. To find the prime factorisation of 98, we can follow these steps:
Start by dividing 98 by the smallest prime number, which is 2. We get 98 ÷ 2 = 49.
Now, divide 49 by the smallest prime number, which is 7. We get 49 ÷ 7 = 7.
Since 7 is a prime number, we stop here.
The prime factorisation of 98 is 2 × 7 × 7, or in exponential form, 2 × 7².
Example: Find the factors of 98.
Solution: The factors of 98 are 1, 2, 7, 14, 49, and 98.
Example: Determine the pair factors of 98.
Solution: The pair factors of 98 are (1, 98) and (2, 49).
Example: What is the prime factorisation of 98?
Solution: The prime factorisation of 98 is 2 × 7 × 7.
In mathematics, factors are numbers that divide another number evenly 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, we can write the factors of 98 as 1 × 2 × 7 × 14 × 49 × 98 or 1 · 2 · 7 · 14 · 49 · 98.
There are different types of factors, including:
Prime factors: These are the factors that are prime numbers.
Composite factors: These are the factors that are composite numbers.
Pair factors: These are the factors that can be multiplied together to get the original number.
Negative pair factors: These are the pair factors where one factor is negative and the other is positive.
Question: What are the factors of 98? Answer: The factors of 98 are 1, 2, 7, 14, 49, and 98.
Question: What is the prime factorisation of 98? Answer: The prime factorisation of 98 is 2 × 7 × 7.
Question: How do you find the factors of a number? Answer: To find the factors of a number, list all the numbers starting from 1 up to the given number and check if each number divides the given number evenly without leaving a remainder.
Question: What is the difference between pair factors and negative pair factors? Answer: Pair factors are the factors that can be multiplied together to get the original number, while negative pair factors are the pair factors where one factor is negative and the other is positive.
Question: How are factors used in mathematics? Answer: Factors are used in various mathematical concepts, such as prime factorisation, finding common factors, solving equations, and determining divisibility.