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.
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.
To find the factors of 240, follow these steps:
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 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.
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.
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).
Example: Find the prime factorisation of 240.
Solution: The prime factorisation of 240 is 2^4 * 3 * 5.
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.
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.
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.
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.