Factors of 147

Factors of 147

Factors are numbers that can be multiplied together to get a given number. In this blog, we will explore the factors of 147 and understand their significance in mathematics.

Answer to Factors of 147

The factors of 147 are: 1, 3, 7, 21, 49, and 147.

How to solve the problem: hints

To find the factors of 147, we can follow these steps:

1. Determine the criteria for judging whether a number is a factor. A factor should divide the given number without leaving a remainder.
2. List all the numbers starting from 1 up to the given number, which is 147 in this case.
3. Use each number as a divisor and verify whether it is a factor by dividing 147 by the number. If the division results in an integer value, then the number is a factor.
4. Finally, collect all the numbers that are factors of 147.

Let's now go through a step-by-step solution to find the factors of 147.

Step-by-step solution

1. We start by listing all the numbers from 1 to 147.
2. Using each number as a divisor, we divide 147 and check if the division results in an integer value.
3. The numbers 1, 3, 7, 21, 49, and 147 satisfy the criteria and are therefore the factors of 147.

Hence, the factors of 147 are 1, 3, 7, 21, 49, and 147.

Pair Factors and Negative Pair Factors of Factors of 147

The pair factors of 147 are the pairs of numbers that multiply together to give 147. In this case, the pair factors are (1, 147), (3, 49), and (7, 21).

Negative pair factors are the pairs of numbers where one number is positive and the other is negative, and their product is equal to 147. For 147, there are no negative pair factors since all the factors are positive.

Prime Factorisation of 147

Prime factorisation is the process of expressing a number as a product of its prime factors. To find the prime factorisation of 147, we divide it by prime numbers until we can no longer divide.

The prime factorisation of 147 is 3 * 7 * 7, where 3, 7, and 7 are all prime numbers.

Solved Examples

1. Example 1: Find the factors of 147. Solution: The factors of 147 are 1, 3, 7, 21, 49, and 147.

2. Example 2: Determine the pair factors of 147. Solution: The pair factors of 147 are (1, 147), (3, 49), and (7, 21).

3. Example 3: What is the prime factorisation of 147? Solution: The prime factorisation of 147 is 3 * 7 * 7.

Factors in Mathematics

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.

Symbols Used to Represent Factors

In mathematics, factors are often represented using the multiplication symbol (*) or by writing the numbers next to each other. For example, the factors of 147 can be represented as 1 * 3 * 7 * 21 * 49 * 147 or simply as 1, 3, 7, 21, 49, 147.

Types of Factors

There are two types of factors: prime factors and composite factors.

1. Prime factors are the factors that are prime numbers. In the case of 147, the prime factors are 3 and 7.

2. Composite factors are the factors that are not prime numbers. In the case of 147, the composite factors are 1, 21, 49, and 147.

FAQs on Factors of 147

Question: What are the factors of 147? Answer: The factors of 147 are 1, 3, 7, 21, 49, and 147.

Question: What is the prime factorisation of 147? Answer: The prime factorisation of 147 is 3 * 7 * 7.

Question: How do I find the factors of 147? Answer: To find the factors of 147, list all the numbers from 1 to 147 and divide 147 by each number to check if it is a factor.

Question: Are there any negative factors of 147? Answer: No, there are no negative factors of 147 since all the factors are positive.

Question: What is the significance of factors in mathematics? Answer: Factors help in understanding the divisibility of numbers, prime factorisation, finding common factors, and solving equations. They are fundamental in various mathematical concepts and calculations.

In conclusion, the factors of 147 are 1, 3, 7, 21, 49, and 147. Understanding factors is essential in mathematics as they play a significant role in various mathematical operations and concepts.