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Factors

Factors of 17 | Prime Factors of 17 | Factor Tree of 17 | Solved Examples

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

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Factors of 17 | Prime Factors of 17 | Factor Tree of 17 | Solved Examples

Factors of 17 | Prime Factors of 17 | Factor Tree of 17 | Solved Examples

Factors of 17: Factors of any number are whole numbers that are completely divided by the given number without leaving any remainder. There are only two factors for the number 17, which are 1 and 17, and these factors are both positive and negative numbers (1, 17 and -1, -17). In this blog, we will discuss the factors of 17, how to calculate the factors of 17, prime factorization of 17, and factors of 17 in pairs, along with some solved examples and FAQs. Scroll down to find out more.

What Are the Factors of 17?

A number is said to be a given number’s factor when it is completely divisible by the given number and leaves zero in the remainder. For example, 1 is the factor of 17, which means when 17 is divided by 1, it leaves zero as the remainder. In other words, if two numbers are multiplied together and their result is 17, then that number is a factor of 17. For example, 17 X 1 = 17. The number 17 has only two factors: 1 and 17.

Note: In order to identify factors of any given number, check if the given number is prime number or not. If the given number is a prime number, then it has only two factors, and they are 1 and the number itself. When the given number is a composite number, then it has more than 2 factors.

Factors of 17 in Pairs

17 is a prime number and it has one pair of positive and one pair of negative factors. The positive and negative pair factors of 17 are given below:

  • Positive pair factors of 17, 17 X 1=17 and 1 X 17=17
  • Negative pai factors of 17, -17 X -1= -17 and -1 X -17= -17
Positive Pair Factors of 17

Negative Pair Factors of 17

How to Calculate the Factors of 17 by Division Method?

In the division method, the factors of 17 can be calculated by dividing 17 by an integer. An integer is a whole number that can be a positive, negative number, or zero. It cannot be a decimal or fraction. If any integer gets divided by 17 completely without leaving any remainder, or in other words, without leaving zero in the remainder, Now, let’s see how to calculate the factors of 17 using the division methods for a sequence of natural numbers:

  • 17 ÷ 1= 17 (Remainder = 0)
  • 17 ÷ 2= 8.5 (can’t be divided by 17, so not a factor of 17)
  • 17 ÷ 3= 5.6 (can’t be divided by 17, so not a factor of 17)
  • 17 ÷ 4= 4.2 (can’t be divided by 17, so not a factor of 17)
  • 17 ÷ 5= 3.4 (can’t be divided by 17, so not a factor of 17)
  • 17 ÷ 6= 2.8 (can’t be divided by 17, so not a factor of 17)
  • 17 ÷ 7= 2.4 (can’t be divided by 17, so not a factor of 17)… and so on.
  • 17 ÷ 17= 1 (Remainder = 0)

Hence, the factors of 17 are 1 and 17 as they are completely divisible and leave zero in the remainder.

How to Calculate Prime Factorization of 17?

The prime factorization of a number is the product of its factors, which are prime. Now let’s discuss the process of finding the prime factors of 17.

  • The factors of 17 are 1 and 17. Now, let’s check if the numbers in the pair factor of the number 17 are prime numbers or composite numbers. If a number in the pair factor is a prime number, then you can leave it as it is as you cannot split it any further. If a number in the pair factor is a composite number, it can be split into their prime factors.
  • Now, in the pair factors of 17, we know that 1 is neither a prime number nor a composite number, so it cannot be split further.
  • 17, which is already a prime number and cannot be split further.
  • Hence, 17 can be written as the product of 1 and 17, i.e., 17 X 1 = 17.
  • Therefore, the prime factorization of the number 17 is 17.
Prime Factorization of 17

Find the Factor Tree of 17

The steps to find a factor tree of 17 are given below:

  • Step 1: Firstly, write the number 17 at the top of the factor tree.
  • Step 2: Now, as a part of the tree’s branches, write down the pair factor of 17. The pair factor pair of 17 is 1 and 17.
  • Step 3: Since 1 is neither a prime nor a composite number, it cannot be spilt further, and 17 is already a prime number, so it cannot be spilt further.

Circling all the branches gives us factors 1, and 17. Therefore, the prime factors of 17 using a factor tree are 1 X 17 = 17.

Factor tree of 17

What Are the Factors of 17 Listed From Least to Greatest?

As the number 17 is a prime number
The factors of 17 are 1 and 17
Hence, the factors of 17 in increasing order will be:
1 and 17.

Solved Examples on Factors of 17

Q 1: Find the product of all the prime factors of 17.
A 1:
Since the factor of 17 is 17, therefore, the product of all the prime factors of 17 is 17.

Q 2: What is the sum of all the factors of 17?
A 2:
To find the sum of all the factors of 17, first find the factors of 17.
The factors of 17 are 1 and 17.
Now, add all the factors of 17, 17+1=18.
Therefore, the sum of all the factors of 17 is the number 18.

Q 3: Find the common factors between 17 and 11.
A 3: The factors of 17 are 1 and 17
Whereas the factors of 11 are 1 and 11.
As both 17 and 11 are both prime numbers, the common factor between them is 1.

Q 4: Find the common factors between 6 and 17
A 4:
Factors of 6 are 1, 2, 3, and 6. 
Factors of 17 are 1 and 17.
Therefore, the common factor between 6 and 17 is 1.

Q 5: What are the common factors between 17 and 68?
A 5:
Factors of 17 are 1 and 17.
Factors of 68 are 1, 2, 4, 17, 34, and 68.
Therefore, the common factors between 17 and 68 are 1 and 17.

FAQs on Factors of 17

Find the factors of 17 and 72.
Factors of 17 are 1 and 17.
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 36 and 72. Therefore, the common factor of 17 and 72 is 1.

Find the factors of 17 and 51.
Factors of 17 are 1 and 17.
Factors of 51 are 1, 3, 17, and 51. Therefore, the common factor of 17 and 52 are 1 and 17.

What are the common factors of 17 and 13?
Factors of 17 are 1 and 17
Factors of 13 are 1 and 13. Therefore the common factor of 17 and 13 is 1. Also, 17 and 13 are both prime numbers.

What are the factors of 17 in pairs?
The number 17 has one pair of positive factors and one pair of negative factors. So, the factors of 17 in pairs are 1, 17 is the positive pair, and -1, -17 is the negative pair of the factor of 17.

Find all the common factors of 17 and 60.
Factors of 17 are 1 and 17.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Therefore, the common factor of 17 and 60 is 1.

What are the greatest common factors of 17, 14, and 5?
Factors of 17: 1 and 17
Factors of 14: 1, 2, 7, and 14
Factors of 5: 1 and 5
The common factor of 17, 15, and 5 is 1.
Hence, the greatest common factor of 17, 15, and 5 is 1.

What are the common factors of 17 and 51?
Factors of 17: 1 and 17
Factors of 51: 1, 3, 17, and 51.
Common factors of 17 and 51 are 1 and 17.
Also, the least common factor of 17 and 51 is 1 and the greatest common factor of 17 and 51 is 17.

We hope this article on factors of 17 is helpful to you. If you have any questions related to this page, ping us through the comment section below and we will get back to you as soon as possible.

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Prerit Jain

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