Factors of 240

Factors of 240

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 240 and understand their properties.

Answer to Factors of 240

The factors of 240 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.

How to solve the problem: hints

To find the factors of 240, follow these steps:

1. Determine the criteria for judging whether a number is a factor. A number is a factor of 240 if it divides 240 without leaving a remainder.
2. List all the numbers starting from 1 up to the given number, which is 240 in this case.
3. Use each number as a divisor and verify whether it is a factor by dividing 240 by the number. If the division results in an integer value, then the number is a factor of 240.
4. Finally, collect all the numbers that satisfy the criteria to obtain the factors of 240.

Step-by-step solution

1. The criteria for judging whether a number is a factor of 240 is that it should divide 240 without leaving a remainder.
2. List all the numbers from 1 to 240: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ..., 240.
3. Use each number as a divisor and verify whether it is a factor by dividing 240 by the number. For example, when we divide 240 by 2, we get 120, which is an integer. Hence, 2 is a factor of 240. Similarly, we can check for other numbers.
4. Collect all the numbers that divide 240 without leaving a remainder: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240. These are the factors of 240.

Pair Factors and Negative Pair Factors of Factors of 240

The pair factors of 240 are the pairs of factors that multiply together to give 240. For example, the pair factors of 240 are (1, 240), (2, 120), (3, 80), (4, 60), (5, 48), (6, 40), (8, 30), (10, 24), (12, 20), and (15, 16).

The negative pair factors of 240 are the pairs of factors where one factor is negative and the other is positive, such that their product is 240. For example, the negative pair factors of 240 are (-1, -240), (-2, -120), (-3, -80), (-4, -60), (-5, -48), (-6, -40), (-8, -30), (-10, -24), (-12, -20), and (-15, -16).

Prime Factorisation of 240

Prime factorisation of a number involves expressing the number as a product of its prime factors. The prime factors of 240 are the prime numbers that divide 240 without leaving a remainder. The prime factorisation of 240 is 2^4 * 3 * 5.

To obtain the prime factorisation of 240, we divide 240 by the smallest prime number, which is 2. We continue dividing the quotient by 2 until we can no longer divide evenly. Then, we move to the next prime number, which is 3, and repeat the process. Finally, we have the prime factorisation of 240.

Solved Examples

1. Example: Find the factors of 240.

   Solution: The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.

2. Example: Determine the pair factors of 240.

   Solution: The pair factors of 240 are (1, 240), (2, 120), (3, 80), (4, 60), (5, 48), (6, 40), (8, 30), (10, 24), (12, 20), and (15, 16).

3. Example: Find the prime factorisation of 240.

   Solution: The prime factorisation of 240 is 2^4 * 3 * 5.

Factors in Mathematics

In mathematics, factors are numbers that divide another 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 240 can be represented as 1 * 240, 2 * 120, 3 * 80, and so on.

Types of Factors

There are different types of factors, including prime factors, composite factors, pair factors, and negative pair factors. Prime factors are the prime numbers that divide a given number, while composite factors are the composite numbers that divide a given number. Pair factors are the pairs of factors that multiply together to give the given number, and negative pair factors are the pairs of factors where one factor is negative and the other is positive.

FAQs on Factors of 240

Question: What are the factors of 240? Answer: The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.