Factors are numbers that can be multiplied together to get a given number. In this blog, we will explore the factors of 65 and understand their properties.
The factors of 65 are: 1, 5, 13, and 65.
To find the factors of 65, we can follow these steps:
Determine the criteria for judging whether a number is a factor. A number is a factor of 65 if it divides 65 without leaving a remainder.
List all the numbers starting from 1 up to the given number, which is 65 in this case.
Use each number as a divisor and verify whether it is a factor by dividing 65 by the number. If the division is exact, without any remainder, then the number is a factor.
Finally, collect all the numbers that are factors of 65.
Let's now go through a step-by-step solution to find the factors of 65.
The criteria for judging whether a number is a factor of 65 is that it should divide 65 without leaving a remainder.
List all the numbers starting from 1 up to 65: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, and 65.
Use each number as a divisor and verify whether it is a factor of 65. We can use math expressions to represent this verification. For example, to check if 5 is a factor of 65, we divide 65 by 5: 65 ÷ 5 = 13. Since the division is exact, without any remainder, 5 is a factor of 65. Similarly, we can check for other numbers.
Finally, collect all the numbers that are factors of 65: 1, 5, 13, and 65.
The pair factors of 65 are the pairs of numbers that multiply together to give 65. In this case, the pair factors of 65 are: (1, 65) and (5, 13).
Negative pair factors are the pairs of numbers where one number is positive and the other is negative, and their product is 65. For 65, there are no negative pair factors since 65 is a positive number.
Prime factorisation is the process of expressing a number as a product of its prime factors. The prime factors of 65 are the prime numbers that divide 65 without leaving a remainder. In this case, the prime factorisation of 65 is: 5 × 13.
Example: Find the factors of 65.
Solution: The factors of 65 are 1, 5, 13, and 65.
Explanation: We followed the steps mentioned earlier to find the factors of 65.
Example: Determine the pair factors of 65.
Solution: The pair factors of 65 are (1, 65) and (5, 13).
Explanation: We found the pairs of numbers that multiply together to give 65.
Example: Express 65 as a product of its prime factors.
Solution: The prime factorisation of 65 is 5 × 13.
Explanation: We identified the prime factors of 65 and expressed it as their product.
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.
In mathematics, factors are often represented using the multiplication symbol (×) or by writing the numbers next to each other. For example, the factors of 65 can be represented as 1 × 65, 5 × 13, or simply as (1, 65), (5, 13).
There are different types of factors, including prime factors, composite factors, and negative factors. Prime factors are the prime numbers that divide a given number without leaving a remainder. Composite factors are the composite numbers that divide a given number without leaving a remainder. Negative factors are the pairs of numbers where one number is positive and the other is negative, and their product is the given number.
Question: What are the factors of 65?
Answer: The factors of 65 are 1, 5, 13, and 65.
Question: How do you find the factors of 65?
Answer: To find the factors of 65, list all the numbers starting from 1 up to 65 and check if they divide 65 without leaving a remainder.
Question: What is the prime factorisation of 65?
Answer: The prime factorisation of 65 is 5 × 13.
Question: Are there negative factors of 65?
Answer: No, there are no negative factors of 65 since 65 is a positive number.
Question: What is the pair factor of 65?
Answer: The pair factors of 65 are (1, 65) and (5, 13).
In conclusion, the factors of 65 are 1, 5, 13, and 65. We can find these factors by listing all the numbers up to 65 and checking if they divide 65 without leaving a remainder. The pair factors of 65 are (1, 65) and (5, 13), and the prime factorisation of 65 is 5 × 13. Factors play an important role in various mathematical concepts and are represented using symbols like × or by writing the numbers next to each other.