Factors of 17

Factors of 17

In mathematics, factors are numbers that divide evenly into another number. In this blog, we will explore the factors of 17 and discuss various concepts related to it.

Answer to Factors of 17

The factors of 17 are 1 and 17.

How to solve the problem: hints

To find the factors of 17, we can follow these steps:

1. Determine the criteria for judging whether a number is a factor. In this case, a factor of 17 should divide 17 evenly without leaving a remainder.

2. List all the numbers starting from 1 up to 17.

3. Use each number as a divisor and verify whether it is a factor by checking if it divides 17 evenly. We can use the modulo operator (%) to check for remainders. If the remainder is 0, then the number is a factor.

4. Finally, we can identify the factors of 17 by listing the numbers that divide 17 evenly.

Let's now provide a concise step-by-step solution using math expressions.

Step-by-step solution

1. Determine the criteria: A factor of 17 should divide 17 evenly without leaving a remainder.

2. List all the numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17.

3. Use each number as a divisor and verify whether it is a factor:

   • 1 is a factor of 17 since 17 ÷ 1 = 17 with no remainder.
   • 2 is not a factor of 17 since 17 ÷ 2 = 8 with a remainder of 1.
   • 3 is not a factor of 17 since 17 ÷ 3 = 5 with a remainder of 2.
   • 4 is not a factor of 17 since 17 ÷ 4 = 4 with a remainder of 1.
   • 5 is a factor of 17 since 17 ÷ 5 = 3 with no remainder.
   • 6 is not a factor of 17 since 17 ÷ 6 = 2 with a remainder of 5.
   • 7 is a factor of 17 since 17 ÷ 7 = 2 with no remainder.
   • 8 is not a factor of 17 since 17 ÷ 8 = 2 with a remainder of 1.
   • 9 is not a factor of 17 since 17 ÷ 9 = 1 with a remainder of 8.
   • 10 is not a factor of 17 since 17 ÷ 10 = 1 with a remainder of 7.
   • 11 is not a factor of 17 since 17 ÷ 11 = 1 with a remainder of 6.
   • 12 is not a factor of 17 since 17 ÷ 12 = 1 with a remainder of 5.
   • 13 is a factor of 17 since 17 ÷ 13 = 1 with no remainder.
   • 14 is not a factor of 17 since 17 ÷ 14 = 1 with a remainder of 3.
   • 15 is not a factor of 17 since 17 ÷ 15 = 1 with a remainder of 2.
   • 16 is not a factor of 17 since 17 ÷ 16 = 1 with a remainder of 1.
   • 17 is a factor of 17 since 17 ÷ 17 = 1 with no remainder.

4. The factors of 17 are 1 and 17.

Pair Factors and Negative Pair Factors of Factors of 17

The pair factors of 17 are (1, 17) since both numbers multiply to give 17. Negative pair factors are also considered, so (-1, -17) is another pair of factors.

Prime Factorisation of 17

The prime factorisation of 17 is simply 17 itself. Since 17 is a prime number, it cannot be expressed as a product of other numbers.

Solved Examples

1. Example: Find the factors of 17.

   • Solution: The factors of 17 are 1 and 17.

2. Example: Determine the pair factors of 17.

   • Solution: The pair factors of 17 are (1, 17) and (-1, -17).

3. Example: What is the prime factorisation of 17?

   • Solution: The prime factorisation of 17 is 17.

Factors in Mathematics

In mathematics, factors are numbers that divide evenly into another number. They are used to understand the properties and relationships between numbers. Factors play a crucial role in various mathematical concepts, such as prime numbers, composite numbers, and factorisation.

Symbols Used to Represent Factors

In mathematics, factors are often represented using the multiplication symbol (×) or a dot (·). For example, we can express the factors of 17 as 1 × 17 or 1 · 17.

Types of Factors

There are different types of factors, including prime factors, composite factors, pair factors, and negative pair factors. Prime factors are numbers that are only divisible by 1 and themselves, while composite factors have additional divisors. Pair factors are two numbers that multiply to give the original number, and negative pair factors include the negative counterparts of the pair factors.

FAQs on Factors of 17

Question: Factors of 17? Answer: The factors of 17 are 1 and 17.