Factors are numbers that can be multiplied together to get a given number. In this blog, we will explore the factors of 196 and discuss various aspects related to them.
The factors of 196 are: 1, 2, 4, 7, 14, 28, 49, 98, and 196.
To find the factors of 196, we can follow these steps:
Determine the criteria for judging whether a number is a factor. A factor should divide the given number without leaving any remainder.
List all the numbers starting from 1 up to the given number, which is 196 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 196 by that number. If the division results in an integer value, then the number is a factor.
Finally, collect all the numbers that are factors of 196.
Let's now go through a step-by-step solution to find the factors of 196.
The criteria for judging whether a number is a factor of 196 is that it should divide 196 without leaving any remainder.
List all the numbers starting from 1 up to 196: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ..., 196.
Use each number as a divisor and verify whether it is a factor by dividing 196 by that number. For example, let's check if 2 is a factor of 196:
196 ÷ 2 = 98
Since the division results in an integer value (98), 2 is a factor of 196.
Similarly, we can check for other numbers as well.
Collect all the numbers that are factors of 196: 1, 2, 4, 7, 14, 28, 49, 98, and 196.
Now that we have found the factors of 196, let's explore some additional concepts related to them.
Pair factors are the factors that can be multiplied together to get the given number. For example, the pair factors of 196 are (1, 196), (2, 98), (4, 49), (7, 28), and (14, 14).
Negative pair factors are the pair factors where one factor is negative and the other is positive. In the case of 196, 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. Prime factors are the factors that are prime numbers.
To find the prime factorisation of 196, we can start by dividing it by the smallest prime number, which is 2:
196 ÷ 2 = 98
Now, we divide 98 by 2 again:
98 ÷ 2 = 49
Since 49 is a perfect square, we can stop here. The prime factorisation of 196 is 2 × 2 × 7 × 7, or in exponential form, 2² × 7².
Example: Find the factors of 196.
Solution: The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196.
Example: Determine the pair factors of 196.
Solution: The pair factors of 196 are (1, 196), (2, 98), (4, 49), (7, 28), and (14, 14).
Example: What is the prime factorisation of 196?
Solution: The prime factorisation of 196 is 2² × 7².
In mathematics, factors are numbers that divide a given number without leaving any 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 196 can be represented as 1 × 196, 2 × 98, 4 × 49, etc.
There are different types of factors, including prime factors, composite factors, and unit factors.
Question: What are the factors of 196?
The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196.
Question: What is the prime factorisation of 196?
The prime factorisation of 196 is 2² × 7², which can also be written as 2 × 2 × 7 × 7.
Question: Are there any negative pair factors of 196?
No, there are no negative pair factors of 196 since all the factors are positive.
In conclusion, the factors of 196 are the numbers that divide 196 without leaving any remainder. We can find these factors by listing all the numbers up to 196 and checking if they divide 196 evenly. The prime factorisation of 196 is 2² × 7², and there are no negative pair factors. Factors play an important role in various mathematical concepts and are represented using symbols like ×.