Factors of 252

Factors of 252

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 252 and understand their properties.

Answer to Factors of 252

The factors of 252 are: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252.

How to solve the problem: hints

To find the factors of 252, follow these steps:

1. Determine the criteria for judging whether a number is a factor. A number is a factor of 252 if it divides 252 without leaving a remainder.
2. List all the numbers starting from 1 up to the given number, which is 252 in this case.
3. Use each number as a divisor and verify whether it is a factor by dividing 252 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 252.

Let's now go through a step-by-step solution to find the factors of 252.

Step-by-step solution

1. We start by listing all the numbers from 1 to 252.
2. Using each number as a divisor, we divide 252 and check if the division results in an integer value.
3. The numbers that satisfy the criteria are the factors of 252.
4. Collecting all the factors, we get the answer: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252.

Pair Factors and Negative Pair Factors of Factors of 252

The pair factors of 252 are the pairs of numbers that multiply together to give 252. For example, the pair factors of 252 are (1, 252), (2, 126), (3, 84), (4, 63), (6, 42), (7, 36), (9, 28), (12, 21), and (18, 14).

The negative pair factors of 252 are the pairs of numbers that, when multiplied together, give -252. Since 252 is a positive number, it does not have any negative pair factors.

Prime Factorisation of 252

Prime factorisation of a number involves expressing the number as a product of its prime factors. The prime factors are the prime numbers that divide the given number without leaving a remainder.

The prime factorisation of 252 is 2^2 * 3^2 * 7. This means that 252 can be expressed as the product of 2 raised to the power of 2, 3 raised to the power of 2, and 7.

Solved Examples

1. Example: Find the factors of 252. Solution: The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252.

2. Example: Find the pair factors of 252. Solution: The pair factors of 252 are (1, 252), (2, 126), (3, 84), (4, 63), (6, 42), (7, 36), (9, 28), (12, 21), and (18, 14).

3. Example: Find the prime factorisation of 252. Solution: The prime factorisation of 252 is 2^2 * 3^2 * 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 252 can be represented as 1 * 2 * 3 * 4 * 6 * 7 * 9 * 12 * 14 * 18 * 21 * 28 * 36 * 42 * 63 * 84 * 126 * 252.

Types of Factors

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

1. Prime factors are the prime numbers that divide a given number without leaving a remainder. In the case of 252, the prime factors are 2, 3, and 7.

2. Composite factors are the composite numbers that divide a given number without leaving a remainder. In the case of 252, the composite factors are 4, 6, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252.

FAQs on Factors of 252

Question: What are the factors of 252? Answer: The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252.

Question: What is the prime factorisation of 252? Answer: The prime factorisation of 252 is 2^2 * 3^2 * 7.

Question: How do you find the pair factors of 252? Answer: The pair factors of 252 are found by listing all the pairs of numbers that multiply together to give 252. For example, (1, 252), (2, 126), (3, 84), (4, 63), (6, 42), (7, 36), (9, 28), (12, 21), and (18, 14) are the pair factors of 252.

Question: What are the symbols used to represent factors? Answer: Factors are often represented using the multiplication symbol (*) or by writing the numbers next to each other. For example, the factors of 252 can be represented as 1 * 2 * 3 * 4 * 6 * 7 * 9 * 12 * 14 * 18 * 21 * 28 * 36 * 42 * 63 * 84 * 126 * 252.

Question: What are the types of factors? Answer: The two types of factors are prime factors and composite factors. Prime factors are prime numbers that divide a given number without leaving a remainder, while composite factors are composite numbers that divide a given number without leaving a remainder.