What Are the Factors of 23? | Prime Factorization and Factor Tree of 23

Factors of 23: The numbers that are completely divisible by 23 without leaving any remainder are the numbers known as factors of 23. In other words, if two numbers are multiplied and their result comes out to be 23, those numbers are factors of 23. Since 23 is a prime number, it has only two factors, with 23 being the highest factor of the number 23. In this article, we will discuss the factors of 23, how to find them, prime factorization, and the factor tree of 23, along with some solved examples.

What Are the Factors of 23?

The factors of 23 can be defined as the numbers which are completely divisible by the number 23, or you can define it as two numbers which, when multiplied with each other, give the result of 23.  The factors of 23 can be listed as 1 and 23. The factors of 23 have both a positive pair and a negative one. For the negative pair of factors of 23, we need to multiply two negative numbers, i.e., (-23) X (-1) =-23.  

Factors of 23 = 1, 23 Positive Pair Factor of 23 = 1, 23 Negative Pair Factors of 23 = -1, -23

Factors of 23 in Pairs

The positive factor pairs of 23 is (1, 23) and the negative factor pairs of 23 is (-1, -23).

How to Find the Factors of 23?

To find factors of 23, we need to determine if the given number is a prime number or not. If the given number is a prime number, then it has only two factors: the original number and 1.

If the given number is a composite number, then it has more than two factors. Here, the given number is 23. As a result, the factors of 23 are 23, 1.

To cross check, we can find factors of 23 using the long division method. The steps to finding factors of 23 using the long division method are explained below.

• Step 1: Divide the number 23 by the sequence of natural numbers. Those numbers which are completely divisible by the number 23 and leave no remainder are the numbers known as factors of 23.
• Step 2: Since 1 and 23 are the only numbers that are divisible by 23, the factors of 23 are 1 and 23.
  • 23/1 = 23 (Remainder = 0)
  • 23/2 = 11 (Remainder = 1)
  • 23/3 = 7 (Remainder = 2)
  • 23/ 4 = 5 (Remainder = 3)
  • 23/23 = 1 (Remainder =0)

Prime Factors of 23

We can find the prime factors of 23 through prime factorization. Let us see the steps below for the prime factorization of 23:

• Step 1: To find the prime factors of 23, using the prime factorization method, we can write the prime factors of 23 as 23 = 1 X 23.
• Step 2: Now that 23 is a prime number, we cannot factor it further because prime numbers do not have factors other than 1 and the number itself.
• Step 3: Therefore, the prime factor of 23 is 23 itself.

What Is the Factor Tree of 23?

We can also find the prime factors of the number 23 using the factor tree method. The steps to finding prime factors of number 23 using the factor tree method are given below:

• Step 1: Place the number 23 at the top of the factor tree and keep splitting until we are left with prime numbers at the end.
• Step 2: Now, as the tree branches, we will write down the pair factors of 23. Here we are using the pair factor 1, 23, as the first branch of 23.
• Step 3: Because 1 and 23 are prime numbers that cannot be divided further, they are the end of the tree branch. 

The factor tree of 23 is given below:

Solved Examples of Factor of 23

Q 1: What are the prime factors of 23?
A 1: If we calculate the prime factors by the prime factorisation method. So, we can write the prime factors as 23= 1 X 23. Since, 23 is a prime number it cannot be split further so the prime factor of 23 is 23.

Q 2: What are all the factors of 23?
A 2: Since, 23 is a prime number it cannot have factors other than 1, as 1 is a factor of all natural numbers, and 23 itself. Therefore, the factors of 23 are 1 and 23.

Q 3: What are all the factor pairs of 23?
A 3: 23 has two factor pairs; positive and negative pair.
The positive pair is 1, 23.
The negative pair is -1, -23.

Q 4: What is the sum of the factors of 23?
A 4: The factors of 23 are 1 and 23
The sum of the factors of 23 is 1+23= 24.
Therefore, the sum of the factors of 23 is 24.

Q 5: Find out the highest common factor of 24 and 8.
A 5: The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
The factors of 8 are 1, 2, 4 and 8
Therefore, the common factor of 24 and 8 is 1.

FAQs on Factors of 23

Find the factor of 23 in pairs.
The number 23 have two factor pairs, one positive and one negative pair.
The positive pair is 1, 23.
The negative pair is -1, -23.

What are the factors of 23 and 29?
The factors of 23 are 1 and 23.
The factors of 29 are 1 and 29.
Therefore, the common factor of 23 and 29 is 1.

Find the lowest and highest factors of 23.
All the factors of 23 are 1 and 23.
Therefore, the lowest factor of is 1, and the highest factor of 23 is 23.

Find the common factors of 23 and 120.
The factors of 23 are 1 and 23.
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Therefore, the common factor of 23 and 120 is 1.

What are the common factors of 23 and 29?
The factors of 23 are 1 and 23.
The factors of 29 are 1 and 29.
Therefore, the common factor of 23 and 29 is 1.

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