Factors Of 17 | Factors Pairs and Prime Factors | Easy Guide

Factors Of 17

The factors of 17 are numbers that divide 17 exactly but do not leave a remainder. The number 17 has only two factors since it is a prime number. It can have positive or negative factors. Here you will learn the factors of 17 in detail.

For instance, the pair factor of 17 can be either (1, 17) or (-1, 17). Multiplying -1 and -17, for example, leads to the original number 17 when multiplying -1 and -17. 

Using the prime factorization method and a few solved examples, you will learn what the factors of 17 are, including the pair and prime factors.

Keep reading, I hope you will learn perfectly.

What are the Factors of 17?

The factors of 17 are the numbers that divide 17 completely and leave 0 as a remainder. Consequently, if two numbers are multiplied together and result in 17, they are factors of 17. 

Since 17 is a prime number, it has only two factors: 1 and the number itself. Therefore, 17 has only two factors, 1 and 17.

Factors of 17: 1 and 17.

Prime Factorization of 17: 17 or 17¹.

What are the Factors of -17?

Factors of -17:  -1 and -17.

To get the product -17, multiply two numbers as follows:

-17 x  1 =  -17

 17 x -1 =  -17

As a result, there are two pairs of factors of -17 as (-17 x 1) and (17 x -1). 

Pair Factors of 17

Whenever two numbers are multiplied together and result in 17, this is referred to as the pair factor of 17. There is one positive pair factor and one negative pair factor in the number 17, and we know it is a prime number.

The following are the negative and positive pair factors for 17:

Positive Pair Factor of 17:

Negative Pair Factor of 17:

This means that there are positive and negative pair factors of 17 respectively (1, 17) and (-1, -17).

Factors of 17 by Division Method

By dividing 17 by different integers, you can find the factors of 17. Those integers are the factors of 17 if they divide 17 without leaving a remainder. Let’s now look at how to find the factors of 17 using the division method.

Let’s divide 17 by 1 and then move on to the other integers.

• 17/1 = 17  (Factor is 1 and Remainder is 0)
• 17/17 = 1  (Factor is 17 and Remainder is 0)

A remainder value is left when we divide 17 by any number other than 1 and 17. This means that the factors of 17 are 1 and 17.

Prime Factorization of 17

17 is written as the product of its prime factors in the prime factorization. Here is how to find the prime factors of 17.

Let’s say we have a pair factor of 17, so (1, 17).

Make sure that both factors are prime numbers or composite numbers. Keep the number as it is if it is a prime number. As a rule of thumb, if the pair factor includes composite numbers, each of the numbers in the factor should be split into its prime factors, and those factors should be written as its prime factors’ products.

As we know, you cannot split 1 into any more primes or composites.

Let’s look at another prime number, 17, as well.

As a result, 17 is written as the product of 1 and 17.

(i.e.) 17 = 1 × 17.

Therefore, the prime factorization of 17 is 17 or 17¹.

Examples

Example 1:

Determine the common factor of 17 and 53.

Solution:

1 and 17 are the factors of 17.

Factors of 53 = 1, 2, 3, 6, 9, 18, 27, and 54.

As a result, 17 and 54 have a common factor of 1.

Example 2:

What are the common factors between 17 and 18?

Solution:

Factors 17 are 1 and 17

Factors of 18 = 1, 2, 3, 6, 9 and 18.

Since 17 is a prime number, 17 and 18 have a common factor of 1.

Example 3:

Determine the common factor between 17 and 24.

Solution:

1 and 17 are the factors of 17.

1, 2, 3, 4, 6, 8, 12, and 24. are the factors of 24.

The common factor of the numbers 17 and 11 is 1 since they are both prime numbers.

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